Abstract Algebra 1 a) Prove that if G is a cyclic group of prime order than...

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Abstract Algebra

1 a) Prove that if G is a cyclic group of prime order than G has exactly two subgroups. What are they?

1 b) Let G be a group and H a subgroup of G. Let x ∈ G. Proof that if for a, b ∈ H and ax = b then x ∈ H. (If you use any group axioms, show them)

Answer 1

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