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2003•Wuhan University JournalRequires access

On the Isomorphism of the Semidirect Product

Xiusheng Liu

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Abstract

Let N,H be two groups, and φ,ψ be two homomorphism from H to Aut(N) of the automorphism group of N. In this paper, we give some condition under which we prove three theorems about the isomorphism between the semidirect product of N by H corresponding to φ and that of N by H corresponding to ψ.Two of the theorems extend two well-known results, respectively.

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What this paper is about

Let N,H be two groups, and φ,ψ be two homomorphism from H to Aut(N) of the automorphism group of N. In this paper, we give some condition under which we prove three theorems about the isomorphism between the semidirect product of N by H corresponding to φ and that of N by H corresponding to ψ.Two of the theorems extend two well-known results, respectively.

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Available abstract

Let N,H be two groups, and φ,ψ be two homomorphism from H to Aut(N) of the automorphism group of N. In this paper, we give some condition under which we prove three theorems about the isomorphism between the semidirect product of N by H corresponding to φ and that of N by H corresponding to ψ.Two of the theorems extend two well-known results, respectively.

Key concepts: Semidirect product, Homomorphism, Isomorphism (crystallography), Mathematics, Automorphism, Group isomorphism, Product (mathematics), Automorphism group

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