Let G, H be groups, and let : G H be a group homomorphism. (a) Show...

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Let G, H be groups, and let : G H be a group homomorphism. (a) Show if is surjective and G is abelian, then H is abelian. (b) Show if p is an isomorphism, then H is abelian if and only if G is abelian. (c) Show if p is an isomorphism, then H is cyclic if and only if G is cyclic. Let G, H be groups, and let : G H be a group homomorphism. (a) Show if is surjective and G is abelian, then H is abelian. (b) Show if p is an isomorphism, then H is abelian if and only if G is abelian. (c) Show if p is an isomorphism, then H is cyclic if and only if G is cyclic.