ash 7. Let A and B be normal subgroups of a group G. Suppose that An B = {e}, where e is the identity of G. Prove that i

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Ash 7 Let A And B Be Normal Subgroups Of A Group G Suppose That An B E Where E Is The Identity Of G Prove That I 1 (132.28 KiB) Viewed 14 times

ash 7. Let A and B be normal subgroups of a group G. Suppose that An B = {e}, where e is the identity of G. Prove that if a E A and b E B, then aba-16-1 E An B. Hence, conclude that ab = ba. (Hint. Can you prove that aba-1 € B? What does this tell you i about aba-16-1?) (b) Prove that if AB = G, then f : A x B + G defined by f ((a,b)) = ab is an isomorphism. CA ona B Copy Copy