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Cauchy's Theorem Problem (Abstract Algebra question)
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.
Homework Statement
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.
Homework Equations
The Attempt at a Solution
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