1) HALACHAH: MAY WOMEN MAKE A "ZIMUN" TOGETHER
OPINIONS: The Gemara quotes a Beraisa that states that women may make a Zimun when they recite Birkas ha'Mazon together. What is the Halachic ruling in this matter?
(a) TOSFOS (DH Sha'ani Hasam) rules that there is no obligation for women who eat together to make a Zimun; rather, they may make a Zimun if they so desire. Accordingly, the common practice today is that women do not make a Zimun. This also appears to be the opinion of RASHI (DH d'Ika De'os).
The SEMAG adds that when a woman eats with a group of men, she is obligated to join the Zimun even according to Tosfos. It is only optional for women to make a Zimun when three or more women eat together without a Zimun of men.
(b) The ROSH (7:4) disagrees with Tosfos for several reasons. First, the Gemara in Erchin (3a) learns that women make a Zimun from a Beraisa that states, "ha'Kol Chayavin b'Zimun," which implies that women are obligated. Second, since a woman is obligated to recite Birkas ha'Mazon (either mid'Oraisa or mid'Rabanan; see Berachos 20b), why would she not be obligated in Zimun? Third, the Gemara concludes that women are "separate minds" ("Ika De'os"); that is, each woman is considered to be like one man with regard to Zimun. This implies that three women have the same obligation of Zimun as three men. Tosfos indeed mentions that one of the Rishonim asked his daughters to make sure to recite Birkas ha'Mazon with a Zimun when eating together without men.
HALACHAH: The SHULCHAN ARUCH (OC 199:7) rules like Tosfos who says that when women eat by themselves, they may choose whether or not to make a Zimun. When they eat together with a group of men, though, they are obligated to join the Zimun.
The BI'UR HALACHAH (DH Nashim) quotes the VILNA GA'ON who rules in accordance with the Rosh and says that women are obligated to make a Zimun even when they eat only with other women. However, he concludes that the accepted practice is for women not to make a Zimun by themselves at all, as Tosfos says. (See also Insights to Erchin 3:2.)
2) TWO PEOPLE MAKING A "ZIMUN"
QUESTION: The Gemara attempts to prove that it is Rebbi Yochanan who maintains that two people may not make a Zimun. The Gemara quotes another statement of Rebbi Yochanan in which he says that when two people eat together, one of them recites Birkas ha'Mazon for both. Rebbi Zeira explains that this means that they may not make a Zimun together.
RASHI (DH v'Amar Rebbi Zeira) explains that Rebbi Yochanan was teaching that two people are not obligated to make a Zimun. This implies, however, that they are permitted to make a Zimun. Why does Rashi say that they are not obligated, when the Gemara is trying to prove that not only are they not obligated, but they are not permitted to make a Zimun?
ANSWER: The TZELACH answers that Rashi is bothered by the following question: Rebbi Yochanan said only that one fulfills his obligation to say Birkas ha'Mazon by listening to another say it. How does Rebbi Zeira infer from Rebbi Yochanan's statement that two people who eat together may not make a Zimun?
In order to answer this question, Rashi understands that Rebbi Yochanan's statement is based on two premises. First, when Rebbi Yochanan said that one person recites Birkas ha'Mazon for both of them, he was referring to a case in which a Talmid Chacham and an Am ha'Aretz eat together. Rashi infers this from the Gemara later that says that when two people eat together, they should each recite Birkas ha'Mazon individually, unless one of them is an Am ha'Aretz. If one is an Am ha'Aretz, then the other one should recite Birkas ha'Mazon for both of them. Second, when three people make a Zimun together, with two listening to the Birkas ha'Mazon of the third, it is considered as though each person says Birkas ha'Mazon on his own (because all participants recite some part of it, even though they do not recite the entire Birkas ha'Mazon).
Therefore, we may conclude that if it is permitted for two people who are both Talmidei Chachamim to make a Zimun, then it should be obligatory for two people, one of whom is an Am ha'Aretz, to make a Zimun -- so that it can be considered that the Am ha'Aretz said Birkas ha'Mazon by himself. From the fact that Rebbi Yochanan said that the Talmid Chacham recites the blessing for the Am ha'Aretz, it is clear that it is not even permitted for them to make a Zimun. If it had been permitted to do so when two Talmidei Chachamim eat together, then in the case of the Am ha'Aretz it would have been obligatory.
3) ONE PERSON WALKED AWAY FROM THE "ZIMUN"
OPINIONS: The Gemara says that if one of three people who ate together leaves the table and walks away, the remaining two may make a Zimun as long as the one who left is close enough that "they call him and he answers." If he leaves a group of ten, however, then they may not make a Zimun until he actually returns to them. What does the Gemara mean when it says that "they call him and he answers"?
(a) RASHI (DH v'Hu d'Kari Lei) explains that the Gemara means that the person who walked away does not have to return in order to join the Zimun. He may stay where he is, listen to the Zimun, and respond "Baruch she'Achalnu...." If he was part of a group of ten people, though, he must come back to his place in order to participate.
The ME'IRI adds that in a case of three or ten people, the one who left the group fulfills his obligation to recite Birkas ha'Mazon in the place where he is standing even though, normally, l'Chatchilah one must recite Birkas ha'Mazon in the place where he ate. Since he is part of the Zimun, he is considered to be "drawn" to the place of the person who is leading the Zimun (and thus it is considered that he recited Birkas ha'Mazon in the place where he ate).
(b) RABEINU CHANANEL explains that the Gemara means that the people who remain at the meal call him and inform him that they are ready to be Mezamen, and he answers that he is coming back (Rabeinu Chananel) or that he is paying attention to their Zimun (RITVA, RA'AVAD as cited by the Me'iri), even though he does not actually respond to their Zimun. Since the third person's verbal response to a Zimun is not absolutely necessary in order for a Zimun to be valid, here it is acceptable even l'Chatchilah for him not to respond.
(c) The RE'AH has an entirely different approach. He explains that the person must return to the table before the group is Mezamen. If he did not walk very far, he may still join the Zimun when he returns. However, if he walked so far that he was no longer able to hear those who remained at the meal, then he may not join the Zimun when he returns. (This applies only if he left without any intention to return. If he left with intention to return, he certainly may join the Zimun when he returns.)
In contrast, a group of ten people may make a Zimun only when no one left at all. (The Re'ah's Girsa is "Ad d'Isa" ("until he is there") in place of "Ad d'Aisi" ("until he comes back").)
4) HALACHAH: SAYING "AMEN" AFTER "BONEH YERUSHALAYIM"
OPINIONS: The Gemara relates that Abaye would say "Amen" loudly after his own blessing of "Boneh Yerushalayim" in Birkas ha'Mazon in order to indicate to the workers that they should return to their work (and not recite the fourth blessing, "ha'Tov veha'Meitiv," of Birkas ha'Mazon, since the fourth blessing is mid'Rabanan). Rav Ashi used to say "Amen" quietly, so that people would not belittle the blessing of "ha'Tov veha'Meitiv" by saying that it is not mid'Oraisa. What is our practice?
(a) The SHULCHAN ARUCH (OC 188:2) rules like the RAMBAM who writes that "Amen" after "Boneh Yerushalayim" should be recited quietly. Since nowadays we do not have workers who omit the last blessing, we should not say this Amen loudly lest people belittle the last blessing.
(b) However, this is not the common practice today. The common practice is not to be careful to say this "Amen" quietly. The REMA (OC 188:2) explains that the reason is because when a group of people recite Birkas ha'Mazon together, and the group responds "Amen" after each blessing that the leader concludes, it is not evident that the leader himself is also responding "Amen" to the blessing. Hence, when one says Birkas ha'Mazon with a group of people, he may say "Amen" aloud. However, when one says Birkas ha'Mazon by himself, he should say "Amen" quietly. Since that is the only blessing to which he says "Amen," it is evident that he is showing that "ha'Tov veha'Meitiv" is mid'Rabanan.
(c) The MISHNAH BERURAH (188:2) explains that we may say Amen out loud even when we recite Birkas ha'Mazon in private. In the times of the Gemara, when workers were permitted (and required) to omit "ha'Tov veha'Meitiv" in order to get back to work, there was a concern that they would become accustomed to omitting "ha'Tov veha'Meitiv" even when they did not have to get back to work. Therefore, "Amen" had to be said quietly so that they would not think that the rest of Birkas ha'Mazon was unimportant. Nowadays, however, we do not have workers who must get back to work immediately after "Boneh Yerushalayim" (as the Shulchan Aruch writes in OC 191:2), and there is no concern that one will belittle the fourth blessing. Therefore, we may say "Amen" out loud.