There has been quite a lot of discussion on this blog in the past on 1 Corinthians 14:34-35, see for example this post. Basically two arguments have been put forward for not understanding it as literal teaching for women to be completely silent in church meetings.
One is to understand that it cannot mean that because that would contradict another part of the same letter, 11:5, and so the meaning must be something like that women should not chatter or ask questions out of turn.
The other argument, originally popularised by Gordon Fee in his commentary on 1 Corinthians, is that these verses are not an original part of Paul’s letter, but an interpolation originally written in the margin.
Today on the Koinonia blog Philip B. Payne has posted Why would 1 Cor 14:34-35 be an interpolation? This is a powerful expression of the second argument, including scholarly references to manuscripts demonstrating that these two verses were long ago recognised as an interpolation. Payne also links to his personal website which has further links to several of his scholarly papers on this subject. Sadly the photographs of manuscripts which he mentions in his Koinonia post are not in the online versions of the papers.
Payne also links to his forthcoming book Man and Woman, One in Christ.