## Sunday, April 21, 2013

### A nice little finite group exercise

Exercise 1: Using the Structure Theorem for Finite Abelian Groups, or otherwise, show that a Sylow $$p$$-subgroup of a finite abelian group is a characteristic subgroup.

Exercise 2: If $$N \triangleleft G$$ is a minimal nontrivial normal subgroup, and is finite and abelian, then $$|N|$$ is a power of a prime.