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  3. let ? : g1 ? g2 be a group homomorphism. (abstract

Let ? : G1 ? G2 be a group homomorphism. (abstract algebra) (a) Suppose H is...

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Let ? : G1 ? G2 be a group homomorphism. (abstract algebra)

(a) Suppose H is a subgroup of G1. Define ?(H) = {?(h) | h ? H}.Prove that ?(H) is a subgroup of G2.

(b) Let ker(?) = {g ? G1 | ?(g) = e2}. Prove that ker(?) is asubgroup of G1.

(c) Prove that ? is a group isomorphism if and only if ker(?) ={e1} and ?(G1) = G2.

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