Suppose that G is a group in which . Prove that is abelian.
So what I need to show is that, in addition to G satisfying closure, associativity, identity and inverse, also satisfies commutativity ( but I'm not sure how to get started.
Suppose that G is a group in which . Prove that is abelian.
So what I need to show is that, in addition to G satisfying closure, associativity, identity and inverse, also satisfies commutativity ( but I'm not sure how to get started.
Merely note that for any arbitrary we have that , and by assumption . So,