Women & Zimmun: Allowed? Required?

Mishna: Three people who ate as one are required to form a zimmun … the Gemara asks: From where are these matters derived, that after a meal in which three diners participated, a zimmun must be recited? Rav Asi said: As the verse states: “Praise God with me, and we will exalt His name together” (Psalms 34:4), i.e., the one reciting the blessing turns to at least two others to praise God together. Rabbi Abbahu said: The source of the mitzva of zimmun is derived from the verse here: “When I call the Name of the Lord, give [plural] praise to our God” (Deuteronomy 32:3).

Women form a zimmun for themselves and slaves form a zimmun for themselves; however, women, slaves, and minors, even if they wish to form a zimmun together, they may not form a zimmun.

And the statement that "even 100 women are comparable to 2 men" -- that applies to matters of prayer gatherings and all matters which pertain to the quorum of 10. And even in this case we evaluate the women as if they were a group of 3. And the same ruling applies to 2. But we would not say that [the 100 women] are comparable to a single man, because they are unable to perform Zimun [with or for men?], as we have learnt "women perform Zimun for themselves." And Rashi explained that they are like 2 for the evaluation of obligation, in that they are not obliged to do Zimun but if they want to they can, and that same ruling applies to 2.

“All are obligated in zimmun” – to include what? [What additional class of people is included in the obligation of zimmun by virtue of the word “all”?] To include women and bondsmen, as it is taught [in a baraita]: “Women recite a zimmun for themselves, and bondsmen recite a zimmun for themselves.”

If Women and Children are obligated in Grace after Meals. Women are obligated to recite Grace after Meals. A doubt exists whether they are obligated from the Torah, and thus are able to fulfill the obligation of men (who listen to their recitation), or if their obligation is merely Rabbinical in origin, and thus can only fulfill the obligation for someone whose obligation is likewise merely Rabbinical.

It is difficult, why are they [women] not accustomed [to recite zimmun]? From what is taught “they recite zimmun” it sounds as though “they are obligated to recite zimmun.” One can answer that “women recite zimmun for themselves” – is if they wish to recite zimmun, they recite zimmun. And this is slightly the meaning of the language is taught afterwards, “women, bondsmen, and minors, if they wish to recite a zimmun – they do not recite a zimmun” … And what is said at the beginning of Arachin (3a), “All are obligated in zimmun” to include women” is said as a voluntary matter and not as an obligatory matter.

Three that ate together as one are required to make a zimun:

Women recite zimmun for themselves, as a reshut [voluntary matter]. But when they eat with the men, they are obligated and discharge their obligation with our zimmun.

One can say that the reason the sages did not wish to impose on them [women] the obligation of birkat ha-zimmun when they are on their own is because it is not so common for them to be proficient in birkat ha-zimmun.

Women and slaves, if they wish to form a zimmun, they may not form a zimmun. Why not? Aren’t they individual minds, which should enable the collective praise of God? That is not the reason, rather it is different there due to promiscuity.

Women, slaves, and minors do not obligate those with whom they ate in a zimmun.

3 women, and also 3 slaves, but not two women or two slaves that join together with 2 men because men have what women and slaves don't have (in terms of a Chiyuv), because women don't talk about Brit, because they were never part of it, and slaves can't say our inheritance.

Since women do not, etc. In actual fact, they do not have a share in the mitzvah of studying Torah either, and the reason why the Rema divided women and slaves into two categories is because slaves do have a share in the covenant. Nevertheless, the women are accustomed nowadays to say על בריתך... They have in mind the covenant of the males that He has engraved in their flesh....

(12) May not be taken into account for uniting. That is if there were only two free men at the meal, women, slaves or children will not have combined with them to complete the required number of three and thus obligate them to unite to bless. This is because women, slaves or children are not obligated to unite to bless.... Even if they wish to unite with them for this purpose they are also not allowed to do so. This is less acceptable than women or slaves uniting to bless on their own... since it is not becoming for men to associate with women and have their group of three completed by means of a woman.... Even for a woman to combine for this purpose with her husband and with her sons is also not proper.... (13) But they may unite to bless on their own. They may elect to do so....

And will fulfil. For just as men can make their blessings serve for other men to fulfil their obligation, they can also make their blessings serve for women to fulfil their obligation. See the Graz, who is of the opinion that if the women wish to separate from the men to unite on their own they are allowed.