Exercise 4.1.14. Let o : G –→ H be a homomorphism. The kernel of o is the setker o =Ф "({ен}) — {g E G:Ф(g) — ен}.Show o is injective if and only if ker o{eg}.

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Answered: Exercise 4.1.14. Let o : G → H be a…

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Exercise 4.1.14. Let o : G → H be a homomorphism. The kernel of o is the set ker o = q-1({eH}) = {g € G: 9(g) = eH}. Show o is injective if and only if ker o = {eg}.