Proof of the fact that non-abelian simple group of finite order has an even number of elements IN Herstein has stated in the books Topics in Algebra that a proof of the above conjecture was given by Walter Feit and John Thompson.(he defines a simple group as one which has no-nontrivial homomorphic images).
Question: Can anyone please show me a proof of the above conjecture using the group theory background in Herstein's text or at least one I can understand?I am currently studying about homomorphisms from there.
Thanks!
 A: This isn't at all an answer to your question, but as you've already seen, you're not going to get one!  
I thought you might be interested to know that there is now a formally verified computer proof of the Feit-Thompson Theorem.  It took six years to produce and was completed just last year.  Here's an article about it.
A: Many decades after the original proof of the theorem was published, the proof was laid out in two quite approachable (at least as far as I have read into them...they came out after I was working in industry) books: Bender and Glauberman's Local Analysis for the Odd Order Theorem and Peterfalvi's Character Theory for the Odd Order Theorem.  By "quite approachable" I mean "quite readable by a graduate student specializing in algebra".  However, their utility for a graduate student may depend on whether the techniques involved are likely to be useful for any open problems, which I am not in a position to judge.
Sufficient background for those books would be the I. Martin Isaacs books Finite Group Theory and Character Theory of Finite Groups.
