Let G be a group, and let a ∈ G be a fixed element. Define a...

Let G be a group, and let a ∈ G be a fixed element. Define a function Φ : G → G by Φ(x) = ax−1a−1.

Prove that Φ is an isomorphism is and only if the group G is abelian.

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Colby Messinger answered 9 months ago

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