• Deracheha Staff; Laurie Novick, Director
Jeffrey Paul Friedman z"l
August 15, 1968 – July 29, 2012
ז"ל יהודה פנחס בן הרב שרגא פייוועל
כ"ב אב תשכ"ח – י' אב תשע"ב
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What is a minyan and what is it for? Who does and doesn't count toward a minyan and why?
God and Communal Prayer
Tefilla offers us the opportunity to stand before God and seek Divine mercy, rachamei. The Talmud Yerushalmi emphasizes the personal elements of this encounter with God by asserting that each of us needs to seek rachamei for ourselves:
Yerushalmi Berachot 3:3
Does it not make sense regarding tefilla that each and every person should request mercy for themselves!?
At the same time, the Talmud teaches us that praying with others holds special value. For example, God does not reject the prayers of the many:[1]
Berachot 8a
Rabbi Natan says: Whence do we know that God does not despise the prayer of the many? For it is said, "Behold God is great and will not despise."
"Great" here works as a synonym for "the many." But neither Rabbi Natan's statement nor its prooftext provide us with any details as to the nature of the "many" required to achieve this result. A second passage suggests the number ten as significant in this context.
Berachot 6a
Ravin bar Rav Ada said Rabbi Yitzchak said: Whence do we know that God is found in the synagogue? For it is said, "God stands in the Lord's assembly [eida]." And whence do we know that ten who pray have the Shechina with them? For it is said, "God stands in the Lord's assembly [eida]."…
Why should the presence specifically of ten invite the Shechina? The Torah offers precedent for ten constituting a minimal quorum for community:[2] Avraham's final bargaining position in his bid to save Sedom is the presence of ten righteous men.[3] The assignment of judges for Benei Yisrael indicates that the lowest level officials were appointed for groups of ten.[4]
The Torah does not detail who counts toward these tens that represent the community, though the prooftext for this Talmudic statement uses the term "eida," which we'll see elsewhere is associated specifically with a group of free adult men. At the same time, the beginning of this passage teaches that God is found in the synagogue irrespective of who is there.
Does the Shechina only appear for groups of ten men?
God’s presence manifests itself in the places where we create sanctity. A minyan seems to be one such instance. Indeed, several Talmudic passages (Berachot 21a, Megilla 23b, discussed below) cite a verse about sanctity to demonstrate that a minyan is required for some elements of prayer:
Vayikra 22:32
And I will be sanctified within Benei Yisrael
In modern times, Rav Moshe Feinstein, among others, firmly maintained that women have no less sanctity than men.
Responsa Iggerot Moshe, OC IV:49
For with respect to sanctity, they [women] are equal to men …
So how do we end up interpreting the Talmudic statement about God's presence dwelling where ten pray as applying exclusively to men?
The answer is that we don't. Returning to the passage about the Shechina in prayer, we see that, in addition to the initial statement that suggests God is present in the synagogue regardless of who is there, the rest of the passage further erodes the uniqueness of the group of ten in meriting God's presence:
Berachot 6a
Ravin bar Rav Ada said Rabbi Yitzchak said: Whence do we know that the Holy One, Blessed be He, is found in the synagogue? For it is said, "God stands in the Lord's assembly [eida]." Whence do we know that ten who pray have the Shechina with them? For it is said, "God stands in the Lord's assembly [eida]."…Whence do we know that three who sit in judgment have the Shechina with them?...Whence do we know that two who sit and learn Torah have the Shechina with them?...Whence do we know that even one who sits and learns Torah has the Shechina with him? … And once it's so even with one, do we need to mention two? With two, their matters are written in the book of remembrance, with one, his matters are not written in the book of remembrance…And once it's so even with three, do we need to mention ten? For ten, the Shechina arrives before them. For three, not till they sit [in judgment].
In other words, the Shechina is present in a number of contexts in which we serve God, and at a range of numbers, starting with one person. It stands to reason, then, that the Shechina is present when ten women pray, too, much as It would be present when a woman learns Torah.
There is a limit to what we can know with any certainty about the Shechina. Based on this passage, it is possible that the Shechina is manifest in a unique way for the prayer quorum of ten men, and that can affect Halacha. That does not suggest, however, that other groups are cut off from the Shechina.
We have seen that communal prayer presents a unique spiritual opportunity. God will not despise such prayer, and will even manifest the Shechina where it takes place.
Halachically, several key elements of prayer require a minyan of ten:
Mishna Megilla 4:3
We do not make an abbreviated communal repetition of Shema [for those who missed saying it], and we do not pass before the aron kodesh [as a prayer leader], and they [the kohanim] do not raise their hands [to bless the congregation], and we do not read from the Torah, and we do not read haftara from the Prophets…with fewer than ten.
A Talmudic passage adds Kedusha to the list,[5] and Masechet Soferim specifies two additional prayers for which ten are necessary:
Masechet Soferim 10:6
…And we do not recite Kaddish and Barechu with fewer than ten.
Why should the quorum consist of ten? Perhaps because this number is the minimum that can be defined as a community, as suggested by the examples we cited earlier from Chumash. Or possibly because of the principle that a gathering of ten ensures the presence of the Shechina.[6]
Both Talmuds use textual connections to explain this mishna,[7] based on Torah verses involving communities of ten. The point of departure is a verse describing the obligation to sanctify (le-kadesh) God's name:
Vayikra 22:32
And you [pl.] shall not desecrate My holy name, and I will be sanctified [ve-nikdashti] within Benei Yisrael, I am God Who sanctifies you [pl.].
This verse is expounded to derive the Torah-level obligation of public martyrdom (kiddush Hashem) in a case where a Jew is being pressured to sin in the presence of ten Jews.[8]
The Talmud also calls the first rituals in this mishna matters of sanctity, "devarim she-bikdusha."
Megilla 23b
From where do we derive these things [in the mishna]? Rabbi Chiyya son of Abba said Rabbi Yochanan said: For the verse says, "And I will be sanctified within [be-toch] the children of Israel” (Vayikra 22:32). Every davar she-bikdusha [matter of sanctity] should not be with fewer than ten. What implies this? For Rabbi Chiyya taught: We learn from "toch"-"toch." Here it is written "And I will be sanctified within [be-toch] the children of Israel." There it is written, "Separate from within [mi-toch] the assembly [eida]” (Bemidbar 16:21). And we learn from "eida"-"eida." For it is written there [regarding the spies], "until when will this wicked assembly [eida] persist?" (Bemidbar 14:27) Just as there [eida] is ten, so too here it is ten.
The Talmud derives the number ten through a two-step, transitive argument.[9]
The verse in Vayikra states that God is sanctified "within," "be-toch," the children of Israel. This word “be-toch” links to the word “toch” when Moshe and Aharon are commanded to separate from "within the assembly," "mitoch ha-eida," during Korach’s rebellion. The word "assembly," "eida," in the verse about Moshe and Aharon next links to the word “assembly" in a different verse that describes “this wicked assembly,” “la-eida ha-ra’a ha-zot.” “Assembly” in this final verse refers to a clearly a defined group: the spies who gave a negative report about the Land of Israel.
Sanctification occurs within an assembly, and an assembly is a group of ten.
The Talmud Yerushalmi presents parallel sets of verses.
Yerushalmi Megilla 4:4
Rav Ba and Rav Yosei in the name of Rabbi Yochanan: It is said here "eida" and it is said there (Bemidbar 14:27) "until when will this wicked assembly [eida] persist?" Just as eida there [in the case of the spies] refers to ten, so too here it is ten. Rabbi Simon said: It says here "toch" and it says there (Bereishit 42:5) "The sons of Israel came to purchase food among [be-toch] those who came [to Egypt]." Just as toch that is said there is ten, so, too, here it is ten…
Unfortunately, the Yerushalmi does not spell out all the verses it has in mind. The first is likely the one we saw earlier with reference to the Shechina. "God stands in the Lord's assembly [eida]."which is linked to the "assembly" [eida] of the spies.
Rav Simon suggests instead that we start from sanctifying God "within" "toch" the Jewish people. "Within," "toch," also appears with reference to the original benei Yisrael, Ya'akov's children (aside from Yosef and Binyamin). This group seems to be a more positive model for our prayer communities than the spies.[10]
In either case, the textual derivation implies that the ten correspond to or stand in for the entire "children of Israel," whether they are the 600,000 who left Egypt, or the millions of today.[11]
Who Counts
Neither Talmud makes any clear statement here about qualifications for who counts toward the quorum of ten, (a minyan), for these rituals. Halachic consensus is that a minyan for matters mentioned in the mishna is constituted of ten free adult men.[12]
Shulchan Aruch OC 55:1
They recite Kaddish. And we do not recite it with fewer than ten free adult males who have grown two hairs [as a sign of maturation], and this is also the law for Kedusha and Barechu, that they are not said with fewer than ten.
How did we arrive at that consensus? The answer is unclear. Here are some of the main possibilities:[13]
I. Example  The nature of the minyan may reflect the nature of the groups mentioned in the Talmud's prooftexts. Shulchan Aruch Ha-Rav bases his understanding of who constitutes a minyan on the spies mentioned by the Babylonian Talmud.
Shulchan Aruch Ha-Rav OC 55
There is no assembly "eida" of fewer than ten, for it is said, "until when will this wicked assembly persist?" Subtract from them [the twelve spies] Yehoshua and Calev, and ten remain. This assembly must all be of free adult males who have grown two hairs [as a sign of maturation], just as the "assembly" that was spoken of there. But women and bondsmen and minors do not join.
Drawing instead on the Talmud Yerushalmi, Ra'avan says those who count for minyan must be like the adult, male, and free sons of Ya'akov.
Ra'avan Berachot 185
For we say, "every davar she-bikdusha [matter of sanctity] should not be said with fewer than ten." We learn it from "And I will be sanctified within the children of Israel.” And we learn toch-toch from "to purchase food among [be-toch] those who came [to Egypt]." There they were ten, as it is written, "And the ten brothers of Yosef went down [to Egypt]." And all of them were men.
II. Midrashic-Style Reading  Another approach to deriving who constitutes a minyan is to apply midrashic methods to the Talmud's prooftexts. Perhaps, for example, the term "benei Yisrael" here specifically excludes benot Yisrael, or women.[14]
This specific argument is debatable, however, because we derive the Torah-level obligation of public martyrdom from a similar midrashic reading of the very same verse,[15] and it is possible that women do count toward the ten needed to create the public for martyrdom.[16] Those who count women toward the quorum for martyrdom may view its requirement for ten as looser than the requirements of devarim she-bikdusha, because the martyrdom ten need not assemble as one cohesive unit. That distinction might explain divergent treatment of this verse in the two contexts.[17]
III. A Third Passage  Tosafot point to another Talmudic passage as the source for not counting women towards a quorum of ten:
Berachot 45b
But behold 100 women are considered comparable to two men, and yet it teaches "women make a zimmun for themselves"!
Tosafot Berachot 45b s.v. But Behold
But behold 100 women are considered comparable to two men: with respect to a group for prayer and for any matter [davar] that is with ten. Even so, we consider them [the women] as three [for zimmun]….Rashi explained it as comparable to two men with respect to [lack of] obligation [in zimmun], for they [three women] are not obligated to recite zimmun [as three men are], but if they want they can recite zimmun
According to Tosafot, the Talmud expresses surprise that women can make a zimmun[18] because it assumes that women are not counted toward a minyan for prayer, or for other matters that require a minyan. The word davar here may be shorthand for davar she-bikdusha, in which case women might still count toward some halachic groupings of ten. According to Tosafot, this passage assumes that women aren't counted in minyan, though it doesn't explain why.
Rashi, however, (quoted within the Tosafot) reads the Talmudic statement differently, and does not directly apply it to tefilla or other contexts.[19]
IV. Obligation  Meiri suggests that counting toward a minyan for a given mitzva is simply a function of obligation in that mitzva.
Beit Ha-bechira of Me'iri, Megilla 5a
Whatever requires ten, there are those who say that once the obligation of women is equal to [the obligation] of men, they count toward the minyan.
That would mean that a woman should count toward a minyan unless her obligation is different from men's. For example, women are exempt from the mitzva of reciting Shema and its berachot, and so could not create the minyan for being pores al-Shema, which includes reciting them.
Given that Meiri views counting for a minyan as dependent on obligation, shouldn't that mean that women could count toward a minyan for communal prayer, since women are obligated in tefilla? Not necessarily. Meiri might understand there to be a distinct halachic obligation in communal prayer from which women are exempt, in which case women would not count towards a minyan for it. (We address this issue in our next installment.)
V. Representation  Minyan  may be a sort of public representative body for the entire Jewish people, a whole greater than the sum of its parts. As we noted above, the language of "within the children of Israel," as applied to a group of only ten men, may support this idea. Within the Torah, public communal representatives are typically adult males. Along these lines, the national censuses described in the Torah counted men eligible for conscription, and further organized them patriarchally by family, as defined by a common father:
Bemidbar 1:2-3
Take a census of the assembly of the children of Israel, according to their families, according to their fathers’ houses, in the number of names, every male by head count. From twenty years old and up, all who go out to the army in Israel, you shall count them according to their legions, you and Aharon.
Levush puts representation into the language of obligation:
Levush OC 55:4
These ten need to be ten adult males ... as it is written (Vayikra 22:32) “And I will be sanctified within benei Yisrael…,” which means that with every davar she-bikdusha [matter of sanctity] they will sanctify me within benei Yisrael. And it is not called “within benei Yisrael” except with ten, based on a gezera shavatoch-toch” … and afterwards a gezera shava of “eida-eida”…. The default meaning of “benei Yisrael” throughout the Torah refers to adult males, and a bondsman or woman or minor do not count [toward a minyan] because they are not obligated in [all] mitzvot. There are those who allow nine in combination with a minor since he is able to reach obligation overall in mitzvot…. But all the great halachic authorities disagree with this and prohibit it, and I have not seen leniency in practice even in a pressing situation.
Levush draws on the central verse “I will be sanctified within benei Yisrael.” He seems to present minyan as a sort of representative body, whereby a group of ten men can represent the entire Jewish people.
Why must a minyan consist entirely of free adult men? Levush offers two, possibly related, reasons. First, he understands the term benei Yisrael as referring primarily to adult males, unless there is a qualification or tradition to the contrary.[20] Second, he maintains that a person who is exempt from mitzvot, even just some of them (e.g., a woman or bondsman), cannot represent someone who is obligated in them.
Lack of obligation is particularly relevant in the prayer context, because some aspects of the prayer ritual, such as the recitation of Shema and its berachot, are considered time-bound mitzvot from which women are exempt.
From the end of Levush's ruling, we learn that assembling a minyan can be difficult, and that halachic authorities sought flexibility in applying the usual qualifications for minyan to the tenth member. Levush rejects flexibility of this sort, and does not even raise the possibility that it would apply to women. He can entertain the question of whether a male minor might theoretically count as a tenth man only because the minor's exemption is temporary. Nevertheless, Levush does not count a minor toward minyan.
Halachic authorities through the ages have been certain that women cannot count towards a minyan. They are not in consensus as to why this should be the case. The explanations offered for why women are not counted in minyan tend to center on technical halachic reasoning, and not on theological or sociological statements about women.
The Tenth
The idea of counting a minor as tenth for minyan comes from the Talmud. A passage in Berachot raises the possibility that a community could include someone who does not meet the age qualification or the qualification of being free as the tenth member of a minyan or for reciting zimmun with God's name.
Berachot 47b-48a
For Rabbi Yehoshua ben Levi said: Even though they said a minor laid in his cradle is not included in [the three] to make a zimmun, we make him an adjunct of the ten [for reciting it with God's name]. And Rabbi Yehoshua ben Levi said: Nine [free men] and a bondsman can join together [for zimmun]. They raised an objection [based on a baraita]: It happened with Rabbi Eliezer that he entered the synagogue and did not find ten [for minyan], and he freed his bondsman and completed the ten. [That implies that] if he frees the bondsman, yes [he counts] and if not, no [he doesn’t]. [Rather, they] needed two [to complete the minyan]. One bondsman he freed and the other was able to help discharge the obligation [while still a bondsman]…And the practical halacha is not like any of these teachings…
It seems that when the quorum lacks only one, and otherwise God's name will not be sanctified in a minyan, there can be room to allow for someone who does not really count for minyan, such as a bondsman, to complete the group. Two bondsmen would be too many to count.
This is not a full-fledged waiving of the qualification, and it has limited application. The disclaimer that "practical halacha is not like any of these teachings" limits it further. Why isn't gender considered as a potential factor to waive? Likely because disqualification based on age is temporary and a bondsman's status is reversible. In contrast, gender is seen as unchanging.
On the basis of this passage, Rabbeinu Tam takes a theoretical position: accepting a minor as the tenth:[21]
Tosafot Ri Sirleon, Berachot 47b, s.v. asher
This is the responsum of Rabbeinu Tam…Rabbi added to their words that even [a minor] laid in his cradle [could count], because the Shechina dwells upon every group of ten. For when we learn "And I will be sanctified," it makes no difference whether minor or adult, so long as there be nine adults, for more than one we don’t say [is admissible] regarding a bondsman, for there is not so much honor of Heaven in that. A bondsman too is included in "And I will be sanctified," for the Shechina dwells upon all who are obligated in mitzvot and are benei berit [included in the covenant or in circumcision]…The end of the Teshuva. Also Rebbe [Ri] responded to me: Even though his honor Rabbeinu Tam permitted making a minor an adjunct for ten [for zimmun] and for prayer without a chumash in his hand, this was not his practice, and he did not actually do this…Also Rebbe [Ri] did not wish to make a minor or a Sefer Torah an adjunct for tefilla
This responsum is difficult to parse. Rabbeinu Tam limits the Talmud's disclaimer to a few cases, leaving room for flexibility. It's not clear, though, why or how counting more than one bondsman or child would detract from "honor of Heaven," when they're both included in the mitzva of davar she-bikdusha, and considered able to draw the Shechina. There is also the mystery of why neither Rabbeinu Tam nor his student, Ri, were prepared to put this ruling into practice.
Unfortunately, Rabbeinu Tam does not relate directly to gender in the responsum, leaving us to speculate whether it could apply to women. If the term "obligated in mitzvot" can refer to a minor, whose obligation is for educational purposes, or to a bondsman, who is exempt from positive time-bound commandments, then it could be said of women. "Benei berit" is perhaps more complicated, since it can either refer to any member of the covenant, i.e. the Jewish people as opposed to idolators, or to anyone who is circumcised. If the latter, then the ruling might not apply to women, which could explain why Rabbeinu Tam did not mention women explicitly.
Rav Simcha of Speyer reportedly maintained that a woman indeed can be counted as the tenth member of a minyan, for prayer or for zimmun:
Mordechai Berachot 173
I found in the name of Rabbeinu Simcha [of Speyer]: A bondsman and a woman can be counted [as tenth for a minyan], whether for tefilla or for "baruch Elokeinu" [in zimmun].
Beit Yosef understands Rabbeinu Simcha's ruling as an attempt to expand Rabbeinu Tam's, on the basis of women's and bondsmen's shared exemption from positive time-bound mitzvot. Beit Yosef rules, however, that neither the age nor gender requirement may be waived in practice, especially since Rabbeinu Tam never acted on his own responsum.
Beit Yosef OC 55
It is written in Mordechai in the name of Rabbeinu Simcha that a bondsman and a woman can [be counted in] the ten for tefilla and birkat ha-mazon. It is clear that this is in accordance with the explanation of Rabbeinu Tam, who ruled like Rabbi Yehoshua ben Levi regarding a single bondsman joining. Rabbeinu Simcha reasoned that this should also apply to a woman, because in every case a woman is equivalent to a bondsman [with respect to exemption from positive time-bound mitzvot]. Since Rabbeinu Tam himself did not want to act this way in practice, who can be lenient in the matter? Thus the practice has been not to count a woman at all.
Shulchan Aruch Ha-Rav notes that Beit Yosef's ruling on these points is widely accepted as halacha, though he is willing to acknowledge those who count a minor in a very pressing situation without protesting their action:
Shulchan Aruch Ha-Rav OC 55:5
There are those who say that a woman, bondsman, or minor cannot become the tenth for a minyan in any situation but all ten must be free adult males who have grown two hairs [as a sign of maturity]…and this is the fundamental halacha. Even so, one should not protest those who are lenient in a pressing situation to count him [a minor] with a chumash in his hand or even without a chumash since they have someone upon whom they can rely…
Shulchan Aruch Ha-Rav does not count women toward minyan and does not say that he would withhold protest if a woman were counted in a minyan in a pressing situation.
In practice, women are not counted for minyan.
How can women feel included in the prayer community without counting for minyan?
Women's not making up a minyan means that a woman who wishes to participate in communal prayer, including devarim she-bikdusha and Torah reading, needs to pray with men. Men's participation in communal prayer, however, does not depend in any way on the attendance of women. This creates an imbalance that can lead to sensitive situations, as when a prayer space is not set up to accommodate women who wish to pray.
Even when there is a welcoming women's section, men may come to synagogue late, leaving the group waiting for a minyan. At those moments, a woman who has made the effort to arrive on time is starkly confronted with the fact that her presence is not counted for minyan. The situation is often further complicated by statements like, "We need one more person to get started," which may make a woman feel invisible or insignificant.
In response to the complexities of this dynamic, and in a bid to make men more aware that women can participate in communal prayer, some communities have resolved to hold off the beginning of tefilla until ten men and ten women are present. However, this practice can put a significant burden on a congregation, and is simply untenable in many communities. It is telling that most communities that have adopted this standard meet only on Shabbat and holidays.
One constructive step that could suit a wide swathe of communities would be to place greater emphasis on men coming on time for minyan, so that no one has to actively count the men who are present while excluding the women there. Sensitivity in this area could go a long way toward improving the atmosphere for women.
Women, too, have a role to play in making communal prayer more inviting for other women. As blogger Alexandra Dunietz suggests, communities can make an effort to ensure that at least one woman attends every prayer service, so that the ezrat nashim is always welcoming to women, regulars or not:[22]
Alexandra Dunietz, "Two Women Make a Quorum"
It occurs to me that when men go to synagogue for minyan, their concern is whether the ninth and tenth man will arrive, and in large congregations, even that rarely poses a problem. Women, on the other hand, wonder about the second woman. In other words, will any other woman be there?...Perhaps we women have a public role in the synagogue today as well, at least for each other. As long as I show up, if a woman comes to the early minyan in my synagogue—whether to recite kaddish or attend a baby naming or hear the Torah reading or answer a compelling need to stand before God away from house or office–she will not be alone.
Even where gender imbalance is a given, as at minyan, the experience of it may vary. All members of a community can contribute to making women feel welcome at communal prayer.
Further Reading
Rav Aryeh Frimer, "Women and Minyan," Tradition 23:4, (Summer 1988), pp. 54-77.

[1] This piece draws heavily on the sources and analysis of Rav Aryeh Frimer, "Women and Minyan," Tradition 23:4, 54-77 (Summer 1988). Available here: http://www.daat.ac.il/daat/english/tfila/frimer2-1.htm
[2] Pirkei Avot, chapter 5, lists other significant uses of the number ten.
Bereishit 18:32
And he said: Please let my Lord not be angry and I will speak even this time. Perhaps there will be found there ten. And He [God] said: I will not destroy on account of the ten.
Shemot 18:25
And Moshe chose men of valor from all of Israel and appointed them as heads of the people: leaders of thousands, leaders of hundreds, leaders of fifties, and leaders of tens.
Berachot 21b
Rav Ada bar Ahava said: Whence do we know that an individual does not recite Kedusha? As it is said, "And I will be sanctified within the children of Israel." Every davar she-bikdusha should not be recited with fewer than ten.
Aruch Ha-shulchan OC 55
Therefore, for Kaddish and Kedusha and Barechu, when there aren't ten, they shouldn't recite it because the Shechina dwells among ten.
[7] These connections apply to the first two cases in the mishna, and arguably to some of the later ones. For the most part, the latter cases have their own derivation to reach the number ten, which may mean that they are not in the same category as davar she-bikdusha. We use the term "connections" here rather than “derivation” because, as Ran explains, these verses may be less derivations than asmachta, Scriptural supports:
Ran on the Rif Megilla 13b (Rif pagination)
These matters are all learned as asmachta. They are rabbinic, because the order of prayer is itself rabbinic.
Sanhedrin 74a-b
All transgressions in the Torah, if you tell a person to transgress them rather than be killed, he should transgress them rather than be killed, except for idolatry, illicit relations, and murder…You might think this true even in public, The verse teaches us " And you shall not desecrate My holy name, and I will be sanctified " How many is public? Rabbi Ya'akov said Rabbi Yochanan said: Public is no fewer than ten…Come and learn, for Rav Yannai brother of Rabbi Chiyya bar Abba taught: We learn from "toch"-"toch". Here it is written, "And I will be sanctified within (be-toch) the children of Israel, and there it is written separate from within (mi-toch) the assembly. Just as there it is ten and they are all Jews, so, too, here it is ten and they are all Jews.
[9] This type of transitive argument usually appears in one step and is known as a gezeira shava. It takes a word or word root that appears in two distinct verses and uses it to apply halachic details of one verse to the halachic discussion of the other.
Rabbeinu Bachya Vayikra 22
Now he will bring a proof from the ten brothers of Yosef, who were righteous, for a matter of sanctity.
[11] In some cases, preference for the number ten may just represent for a group large enough for an act in their presence to be considered public, as when halachic authorities express a preference for ten for lighting Chanuka candles in the synagogue. In these cases, women may count for the ten. See, for example, Ben Ish Chai here:
Rav Pe'alim II OC 62
Regarding the law of the Chanuka candle, which we light and recite a beracha over in synagogue in order to publicize the miracle …For one can say that it works for women to combine [with men to a quorum of ten] in order to publicize the miracle.
[12] We see explicit mention of this as early as the Ge'onic period. See, for example, Siddur Rav Sa'adya Ga'on, available here: https://hebrewbooks.org/pdfpager.aspx?sits=1&req=20685&st=%u05D6%u05DB%u05E8%u05D9%u05DD&_rnd=0.6051665865818916
Siddur Rav Sa'adya Ga'on
The minimum number of a tzibbur is ten men who have reached puberty.
[13] See Frimer, "Women and Minyan," Tradition 23:4, note 63, for references to more explanations.
Orchot Chayyim I Laws of Tefilla 75
They all need to be men and no women can be counted, as it is written "And I will be sanctified within the benei Yisrael [the sons of Israel]."  And not benot Yisrael [the daughters of Israel].
[15] See note 8 above.
Pitchei Teshuva YD 157:7
Also in the matter of whether women count for this: perhaps we say that they are excluded based on the language “benei Yisrael” and not “benot Yisrael.” But apparently it means specifically Yisrael [of Israelite descent] and not converts, as [suggested] in Sota 26a, that “benei Yisrael” means to exclude converts. Here, it is written, “and I will be sanctified within benei Yisrael, and perhaps here too [as in Sota] there is some inclusion [for converts].
Responsa Radbaz 4:92
The meaning of public is like when ten Jews know of the matter, even though they are not present during the event.
Responsa Yabi'a Omer IV:9
…It would seem that one can say that devarim she-bikdusha are different, with respect to all the ten needing to be together….But regarding martyrdom, we do not require that they be together…One cannot compare the law of martyrdom to devarim she-bikdusha, for women do not count toward devarim she-bikdusha.
Iggerot Moshe, however, does not seem to make this distinction:
Responsa Iggerot Moshe OC I:23
Just as he is obligated in martyrdom to sanctify God's name even in front of ten heretics and violators of Halacha if they, too, are Jews…If so, it must be that in the matter of reciting devarim she-bikdusha that [Shabbat violators] count [toward the minyan of ten].
[18] We plan to discuss zimmun in a forthcoming piece.
[19]He reads the Talmud as expressing surprise that women can make a zimmun voluntarily, even though women do not make an obligatory zimmun. This reading applies the Talmud's statement only to zimmun.
[20] This reason is debatable. Magen Avraham, for example, writes the opposite:
Magen Avraham 46:9
For the entire Torah was said in masculine language, and even so a woman is included….
The phrase “benei Yisrael” can mean either ‘sons of Israel’ or ‘children of Israel.’ Sometimes the Torah refers to all Jews as a group with this or similar terms and sometimes it explicitly distinguishes women from men. In ambiguous cases, like “benei Yisrael" in the verse about sanctification, our sages often stipulate that one meaning is correct. Whether or not females are included in a phrase like this varies from verse to verse. It depends on context and tradition. Levush here assumes that “benei” typically refers only to males, but others would disagree, leaving this an open question.