I have an abstract algebra question I'm stuck on: If G is an abelian group and n is an element of N, show phi: G -> G defined by g -> g^n is a group homomorphism. That statement above needs to be proved, how would I prove it?

I have an abstract algebra question I'm stuck on: If G is an abelian group and n is an element of N, show phi: G -> G defined by g -> g^n is a group homomorphism. That statement above needs to be proved, how would I prove it?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 21E

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I have an abstract algebra question I'm stuck on:

If G is an abelian group and n is an element of N, show phi: G -> G defined by g -> g^n is a group homomorphism.

That statement above needs to be proved, how would I prove it?

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