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  3. 3 lemma let f gh and g hk be homomorphisms...

Question: 3 lemma let f gh and g hk be homomorphisms...

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3. Lemma. Let f G-H and g HK be homomorphisms; assume f is surjective. Ifxo e G, and if ker g is the least normal subgroup of H containing f(xo), then ker(g o f) is the least normal subgroup N of G containing ker f and xo Proof. Show that f(N) is normal; conclude that ker(g o f)f(kerg) C

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