Question #350793

2.7. If G is a group such that (ab)2 = a2b2 for all a, b ∈ G, then show that G must be abelian.


1
Expert's answer
2022-06-21T12:30:40-0400

abab=a2b2abab=a^2b^2 apply a1a^{-1} from left and b1b^{-1} from right. We obtain ba=abba=ab for all a,bGa,b\in G. Hence GG is abelian.


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