(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

show that a group G is abelian if g^2 = 1 for all g in G. Give an example showing that converse is false.

3. The attempt at a solution

Suppose g^2 = 1.

gg = 1,

(g^-1)gg = g^-1

g = g^-1 -- means self inverse. but I'm not sure how to show G is abelian..

and I don't know how I find counterexample.

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# A group G is abelian if

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