Let G be a cyclic group generated by an element a. a) Prove that if an...

Let G be a cyclic group generated by an element a.

a) Prove that if aⁿ = e for some n ∈ Z, then G is finite.

b) Prove that if G is an infinite cyclic group then it contains no nontrivial finite subgroups. (Hint: use part (a))

Expert Solution

Colby Messinger answered 1 year ago

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