Need Help with Graduate Algebra Problems?

[mthhtm33]

I am trying to learn Modern algebra on my own and am having some difficulties without having a solution manual handy. I am studying Algebra by Larry C. Grove. I'd like to post problems and if anyone can provide solutions, that would be greatly appreciated!

1) If x and y are commuting elements in a group G, show |xy| divides LCM (|x|,|y|); equality holds if <x> intersect <y> = 1.

2) If P is a p-Sylow subgroup of G, show that Ng(Ng(P)) = Ng(P).

Thanks!

 

[Mark44]

The rules of this forum prohibit giving solutions to problems (see Rules).

On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.​

If you show what you have tried, though, there are quite a few people who can steer you in the right direction.