For any Abelian group G and any positive integer n, let Gn
Chapter 8, Problem 48E(choose chapter or problem)
For any Abelian group G and any positive integer n, let Gn = {gn | g ? G} (see Exercise 17, Supplementary Exercises for Chapters 1– 4). If H and K are Abelian, show that (H ? K)n 5 Hn ? Kn.Reference:Let G be an Abelian group and let n be a fixed positive integer. Let Gn = {gn | g ? G}. Prove that Gn is a subgroup of G. Give an example showing that Gn need not be a subgroup of G when G is non-Abelian. (This exercise is referred to in Chapter 11.)
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