Gemara

(Rav Yosef): Rav lashes one who is Mekadesh through Bi'ah.... and one who lives in his mother-in-law's house.

Question: Is he lashed only if he lives there, but not for passing by?! Rav Sheshes lashed a man for passing by his mother-in-law's porch!

Answer: That was a special case. He was suspected of Bi'ah with her.

(Chachamim of Neharde'a): Rav lashes only one who is Mekadesh through Bi'ah.

81a (Rav Ashi): We lash a single girl who was secluded, but not a married woman, lest people say that her children are Mamzerim.

Mar Zutra would lash (married women) and announce that this was only for seclusion, not for Bi'ah.

Rav Ashi: Perhaps one will hear about the lashes, but not the announcement.

(Rabah): If Ba'alah b'Ir (a woman's husband is in town), we are not concerned for seclusion with her.

Rav Bivi visited Rav Yosef. (Rav Bivi was in the second story.) Rav Yosef commanded to remove the ladder (lest Rav Bivi descend and be secluded with Rav Yosef's wife.)

Question: Rabah taught that if Ba'alah b'Ir, we are not concerned for seclusion!

Answer: This did not apply, for Rav Bivi was intimate with Rav Yosef's wife.

(Rav Kahana): If men are in an inner room, and women are in an outer room, we are concerned for seclusion (lest a man enter the women's room). If it is vice-versa, we are not concerned.

A Beraisa teaches just the opposite!

Abaye: Out of doubt, we must be stringent and forbid both.

At gatherings, Abaye and Rava would make a wall of flasks or reeds between the men and women. (If a man went to the women, he would be heard.)

Sukah 25b - Question: Why are a Chasan and his friends exempt from Sukah? They can rejoice in the Sukah!

Answer (Abaye): We are concerned for seclusion.

Rishonim

Rif and Rosh (4:24): If Ba'alah b'Ir, we are not concerned for seclusion with her.

Rambam (Hilchos Isurei Bi'ah 22:12): If Ba'alah b'Ir, we are not concerned for seclusion, for she fears her husband. One intimate with her, e.g. they grew up together or she is his relative, may not be secluded with her even if Ba'alah b'Ir.

Rashi (81a DH Ba'alah): If Ba'alah b'Ir, we are not concerned for seclusion to lash her, for she fears lest her husband come.

Rebuttal (Tosfos 81a DH Ba'alah): Rashi connotes that seclusion is forbidden, just we do not lash for it. If so, why did the Gemara ask about Rav Bivi? Rather, she may be secluded when Ba'alah b'Ir.

Question: Even if her husband is not in the city, we do not lash a married woman for seclusion, lest people say that her children are Mamzerim!

Answer #1 (Bach EH 22 DH Ishah): We do not lash a married woman, but we lash the man secluded with her, unless Ba'alah b'Ir.

Rebuttal and Answer #2 (Taz EH 22:7): The Torah equates men and women for all punishments! Rather, we may lash a married woman without children.

Note: All agree that the Torah equates men and women for punishments. Here, Chachamim had a reason to distinguish! Perhaps the Taz holds similarly to what he says elsewhere (regarding Milah on Shabbos), that Chachamim would not forbid something that the Torah explicitly permits.

Answer #3 (Binas Adam (on Chachmas Adam) Beis ha'Nashim 17(27)): Rashi means that when Ba'alah b'Ir, there is no Isur worthy of lashes.

Answer #4 (ha'Makneh 81a DH Ba'alah): Rabah holds like Rav Yosef (12b), who said that Rav lashes one who lives in his mother-in-law's house (even if she is married). Rav Ashi, who says that we do not lash a married woman, holds like Chachamim of Neharde'a (12b), who disagree.

Defense #1 (of Rashi - Taz, ibid.): Also Rashi permits seclusion. Whenever it is forbidden we lash, except for a married woman. Rashi explains that the discussion is only about lashes, but surely we do not forbid to her husband.

Defense #2 (Binas Adam, ibid. and Pnei Yehoshua 81a DH Ba'alah): The Gemara asked, if seclusion is not mid'Oraisa (or so severe) when Ba'alah b'Ir, why was Rav Yosef so stringent to remove the ladder lest they come to such a situation?!

Rebuttal (and Defense #3 - ha'Makneh, ibid.): We are concerned when men and women are in an inner and outer room (or vice-versa) lest they come to be secluded. This is like the case with Rav Bivi! Rather, Rashi compares this to a Nochri left with wine. If he knows that the Yisrael will be away for a while, he is not afraid to touch the wine, unless the Yisrael comes in and out. Here also, we forbid. Rabah taught Stam, even if her husband said that he will not return for a while. Surely, he only exempts from lashes. We forbid men and women in an inner and outer room, and Abaye would make a wall between men and women. Surely, this is even Ba'alah b'Ir for one of the women! Rashi forbids only when he said that he will not return for a while. The Gemara asked about Rav Bivi, for Rav Yosef did not say that he was leaving. Devorah sat under a palm tree when judging Yisrael, due to seclusion (Megilah 14a), even though presumably Ba'alah b'Ir.

Or Some'ach (Hilchos Isurei Bi'ah 22:8): A man may not be secluded with women even if Ba'alah b'Ir for one of them. The Rambam (Halachah 8) permits seclusion with many women only if one of their husbands is there. It does not suffice that Ba'alah b'Ir for one of them! One may be with the woman for whom Ba'alah b'Ir, but the other women are not ashamed in front of her, so she is not a guardian for them. Perhaps the Rambam discusses a man intimate with the women, so the Heter of Ba'alah b'Ir does not apply.

Note: This implies that Ba'alah b'Ir applies even when she is not at home, unlike Binas Adam (below).

Poskim

Shulchan Aruch (EH 22:8): If Ba'alah b'Ir, we are not concerned to be secluded with her, for she fears her husband. If a man is intimate with her, e.g. they grew up together or she is his relative, or if her husband warned her not to be secluded with him, he may not be secluded with her even if her husband is in the city.

Bach (ibid.): The Tur and Rambam permit seclusion. The Ran (33a) explains like Rashi. We are stringent like them, unlike the Shulchan Aruch.

Beis Yosef (DH Ishah, citing Terumas ha'Deshen 244): Ba'alah b'Ir does not permit if her husband warned her not to be secluded with him.

Birkei Yosef: There is a proof for Rashi from the Yerushalmi and Sukah 25b. (We are concerned lest the Chasan descend for his needs and someone will be secluded with the Kalah, even though Ba'alah b'Ir.)

Binas Adam (ibid.): The Torah forbids only Yichud of one man and one woman. Everything else is mid'Rabanan. Therefore, in other cases one may rely on the majority of Poskim who permit, if Ba'alah b'Ir for one of the women. This is only in her house. She does not fear her husband in another house, for he does not know where she is. The Heter is not because she fears lest he come during Bi'ah. This would apply even if the man is intimate with her! Rather, she fears lest her husband come and see her secluded with a stranger, and assume that it was for Zenus. He will investigate, and might learn about the Bi'ah. He will not be aroused to investigate if she is secluded with someone intimate with her, or if he authorized her to go to the house.