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.

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