Group homomorphism and abelian groups

Reference no: EM13124380

Group Homomorphism and Abelian Groups
Let phi: G ---> H be a group homomorphism. Show that phi[G] is abelian if and only if for all x, y in G, we have xyx^(-1)y^(-1) in ker(phi).

proving (=>) seems almost obvious since if it is abelian that means xyx^(-1)y^(-1) = xx^(-1)yy^(-1)=ee which is in the kernel, but I'm not sure about how to do the reverse (<=) and show that phi is abelian?

Reference no: EM13124380

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