If G is any group, define $:G->G by $(g) = g^-1. Show that G is abelian if an only if $ is a homomorphism.© BrainMass Inc. brainmass.com March 4, 2021, 5:52 pm ad1c9bdddf
If G is abelian, then for any x,y in G, we have xy=yx. ...
This is a proof regarding homomorphisms and Abelian groups.