The following is from Adam Clarks Commentary on the Bible. His comment on the Law in the last paragraph is echoed by Henry and others.
1Co 14:34 -
Let your women keep silence in the churches - This was a Jewish ordinance; women were not permitted to teach in the assemblies, or even to ask questions. The rabbins taught that "a woman should know nothing but the use of her distaff." And the sayings of Rabbi Eliezer, as delivered, Bammidbar Rabba, sec. 9, fol. 204, are both worthy of remark and of execration; they are these: ישרפו דברי תורה ואל ימסרו לנשיםyisrephu dibrey torah veal yimsaru lenashim, "Let the words of the law be burned, rather than that they should be delivered to women." This was their condition till the time of the Gospel, when, according to the prediction of Joel, the Spirit of God was to be poured out on the women as well as the men, that they might prophesy, i.e. teach. And that they did prophesy or teach is evident from what the apostle says, 1Co_11:5, where he lays down rules to regulate this part of their conduct while ministering in the church.
But does not what the apostle says here contradict that statement, and show that the words in chap. 11 should be understood in another sense? For, here it is expressly said that they should keep silence in the church; for it was not permitted to a woman to speak. Both places seem perfectly consistent. It is evident from the context that the apostle refers here to asking questions, and what we call dictating in the assemblies. It was permitted to any man to ask questions, to object, altercate, attempt to refute, etc., in the synagogue; but this liberty was not allowed to any woman. St. Paul confirms this in reference also to the Christian Church; he orders them to keep silence; and, if they wished to learn any thing, let them inquire of their husbands at home; because it was perfectly indecorous for women to be contending with men in public assemblies, on points of doctrine, cases of conscience, etc. But this by no means intimated that when a woman received any particular influence from God to enable her to teach, that she was not to obey that influence; on the contrary, she was to obey it, and the apostle lays down directions in chap. 11 for regulating her personal appearance when thus employed. All that the apostle opposes here is their questioning, finding fault, disputing, etc., in the Christian Church, as the Jewish men were permitted to do in their synagogues; together with the attempts to usurp any authority over the man, by setting up their judgment in opposition to them; for the apostle has in view, especially, acts of disobedience, arrogance, etc., of which no woman would be guilty who was under the influence of the Spirit of God.
But - to be under obedience, as also saith the law - This is a reference to Gen_3:16 : Thy desire shall be to thy husband, and he shall rule over thee. From this it is evident that it was the disorderly and disobedient that the apostle had in view; and not any of those on whom God had poured out his Spirit.