Let G, Q be groups, e: G → Q a homomorphism. Prove or disprove the following. (a) For every normal subgroup M « G, ɛ(M) is a normal subgroup of Q. (b) For every normal subgroup N

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4. Let G, Q be groups, ɛ: G → Q a homomorphism. Prove or disprove the following.
(a) For every normal subgroup M < G, ɛ(M) is a normal subgroup of Q.
(b) For every normal subgroup N<Q, ɛ-1(N) is a normal subgroup of G. (Recall
that e-(N) = {g E G|E(g) E N}.)
Transcribed Image Text:4. Let G, Q be groups, ɛ: G → Q a homomorphism. Prove or disprove the following. (a) For every normal subgroup M < G, ɛ(M) is a normal subgroup of Q. (b) For every normal subgroup N<Q, ɛ-1(N) is a normal subgroup of G. (Recall that e-(N) = {g E G|E(g) E N}.)
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