关于半直积同构的注记

Notes on the isomorphism of the semidirect product

从半直积的定义出发,给出了当群H或当从群H到N的自同构群Aut(N)的两个同态φ,ψ满足一定条件时半直积N∝φH与N∝ψH同构的两个定理,而其中一个定理是一个已知结果的推广.

In this paper, we give two theorems about the isomorphism between the semidirect product of N by H corresponding to φ and that of N dy H corresponding to ψ, which the group H or two homorphism φ,ψ from the group H to the Aut(N) satisfies certain condition. One of the theorem extends a well-known result.