Let G be an abelian group and n be a fixed positive integer. LetH={gn|g∈G}andK={x∈G|xn =e},show tha...

Question

Question

Let G be an abelian group and n be a fixed positive integer. LetH={gn|g∈G}andK={x∈G|xn =e},show tha tH<G and K<G.

Extra challenge: Show that the statement may not be true when G is not abelian

Answer 1

Answer #1

GiS a 슨H S6 H İ closed under muR4iplicahơn SContoins idantit emen s o Subgroep Gi » Hnca 九 clesed undax ultiplictian. Cenhoin

.

If you have any doubt or need more clarification at any step please comment.

Answer 2

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