SOLUTION: Let G be a group such that x^2 = e for all x ∈ G. Show that G is abelian.

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Question 1018437: Let G be a group such that x^2 = e for all x ∈ G. Show that G is abelian.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
For all , we have since x*y produces another element in the group.

If we consider the expression , note that y*y = e, so the expression reduces to . So for all

However since and are both inverses of x*y in G, we must have that for all x,y in G.