Let (A, B) be two groups. What are the relations between (x, x^{prime}, x^{prime prime}) in (A)

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Let \(A, B\) be two groups. What are the relations between \(x, x^{\prime}, x^{\prime \prime}\) in \(A\) that are preserved by a group homomorphism \(h: A ightarrow B\) ?

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