Let $\phi $ be an isomorphism from G onto a group G'.Then For any element prove a and b in G, a and b commute if and only if $\phi(a) $and $\phi (b)$ commute.
2026-03-30 06:29:07.1774852147
Property of isomorphism
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Welcome to MSE! An isomorphism is merely a relabeling of the elements. Here, let $a,b\in G$. Then we have $\phi(ab) = \phi(a)\phi(b)$ and $\phi(ba)=\phi(b)\phi(a)$. So $a,b$ commute if and only if $\phi(a)\phi(b)$ commute.