Hi everyone, I have a couple of problems:

1. Find up to isomorphism, all abelian groups of order 32.

2. Prove that no group of order 56 is simple. Hint: use the Sylow Theorems.

3. Let G be a group of order 35: a) Prove that G has only one 5-Sylow and one 7-Sylow that is, G(5) and G(7) respectively. b) Deduce that G is cyclic.

Thanks for the help.