|The gemara (Brachos 45b) says that women and men cannot be counted together to form a Mizuman for Birchas HaMazon. The opinion of the Vilna Gaon is that three women eating together without any men present have an obligation to Bench BiMizuman. Furthermore says the Vilna Gaon in places where it is not customary for women to form a Mizuman, women should make sure not to eat in groups of three because that would obligate them to make a Mizuman.|
Rav Moshe Shternbuch (end of 4:51) asks if women want to make a Mizuman together even though it is not customary, is it permissible. He answers that it is not advisable for a number of reasons. First he says, it comes off as arrogant. Additionally he says that there is an Issur of Lo Sisgodadu for a public to act not in accordance with the customs of the city. Since three people is called a public and women are not Noheg today to make a Mizuman there is a question of Lo Sisgodadu.
Lastly he says Zimun is considered a Bracha even though there is no Shem and Malchus in it. This being the case according to Rebbi Akiva Eiger it would be considered a Bracha Livatala according to the opinions that three women do not form a Zimun. Therefore advise Rav Shternbuch, it is better to be rewarded for abstaining and honoring the Minhag of Klal Yisroel, rather than be Machmir in accordance with an opinion of the Vilna Gaon that was never accepted.
Important Note: We bring this tshuvah as a starting point for discussion and not to convey any halacha. We try to convey the Tshuva to the best of our ability. We admit that our understanding may not be accurate. One should learn the tshuva to verify the accuracy of our interpretation. Please understand that this Tshuva may not be the final word on this topic. One should consult a Rav before drawing any conclusions.