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

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

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

(b) Let ker(φ) = {g ∈ G1 | φ(g) = e2}. Prove that ker(φ) is a subgroup of G1.

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

Expert Solution

Colby Messinger answered 2 years ago

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