Halacha Orach Chaim 186

There is a question among the Rishonim if women are obligated to recite Birchas Hamazon according to a Rabbinic law, or if their obligation is from the Torah just like men.

Because there is a question if women have the same obligation as men, there are several differences that come between them. For example, women cannot recite Birchas Hamazon for men. This is because their obligation may be different. However, a man that did not eat enough to require reciting Birchas Hamazon according to Torah law, will be permitted to listen to women recite Birchas Hamazon. The reason for this is because the man does not have a stricter obligation than women in this scenario.

In addition, there is a discussion among the Poskim if women should recite Birchas Hamazon when they are in doubt if it was said. Men are required, as it is a question regarding a Torah obligation. According to the Shar Efraim and Chaye Adam, women should also recite Birchas Hamazon when in doubt. According to Rebbi Akiva Eiger and the Birchei Yosef, women should not recite Birchas Hamazon when in doubt. The Chofetz Chaim concludes that women who would like to recite Birchas Hamazon when in doubt, are permitted, and we should not protest them. From his language it seems clear that the Chofez Chaim would not obligate them outright.

Reb Shlomo Zalman Aurbach rules that it is worthwhile to require women to recite Birchas Hamazon when in doubt, so Birchas Hamazon will not become light in their eyes.