关于半直积同构的一点注记

Abstract

给定一个有限群N和H,满足Gφ=N■φH和Gψ=N■ψH,在互素的前提下,给出了半直积同构的一个充分必要条件.由此给出了当算子群是循环群时,计算半直积同构类个数的一个方法.作为上述结论的应用,简明地算出了24阶群的完全同构分类.

Let Gφ=NφH and Gψ=NψH be two semi-direct products of N and H.We give a sufficient and necessary condition for Gφ≌Gψ.This offers a way to calculate the number of different Gφ(up to isomorphism).If H is a cyclic group,we have another way to calculate the number of different Gφ(up to isomorphism).As a application,we have a simple way to calculate the isomorphic types of groups of order 24.