(adsbygoogle = window.adsbygoogle || []).push({}); Cauchy's Theorem Problem (Abstract Algebra question)

1. The problem statement, all variables and given/known data

I've been thinking about this problem for a couple days now, and I don't even know how to approach it. The problem is:

Let G be a group of order (p^n)*m, where p is a prime and p does not divide m. Suppose that G has a normal subgroup P of order p^n. Prove that f(P)=P for every automorphism 'A' of G.

I can't even convince myself that the question is true, then alone a method on how to show it. Any point in the right direction would help me a ton. Thanks.

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Cauchy's Theorem Problem

**Physics Forums | Science Articles, Homework Help, Discussion**