Conjugate subgroups homomorphisms and isomorphisms

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Reference no: EM13124438

Direct Products of Groups, Conjugate Subgroups, Homomorphisms and Isomorphisms

Assume that K is a cyclic group, H is an arbitrary group and f1 and f2 are homomorphisms from K into Aut(H) such that f1(K) and f2(K) are conjugate subgroups of Aut(H). If K is infinite, assume f1 and f2 are injective. Prove by constructing an explicit isomorphism that (H x_f1 K) is isomorphic (H x_f2 K)

Reference no: EM13124438

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