素数幂阶子群对有限群结构的影响

The influence of prime power orders of subgroups on the structure of fininte groups

假设G是有限群.子群H称为G的H-子群,如果对任何g∈G有NG(H)∩Hg≤H.用H(G)表示G中所有H-子群的集合.本文讨论某些素数阶子群和4阶循环子群是H-子群的群的结构.

Let G be a finite group. A subgroup H of G is called an -subgroup of G if the following condition is satisfied ：No（H） AH^g ≤H for all g ∈ G. Let （G） denote the set of all -subgroups of a finite group G. The aim of this paper is to investigate the structure of finite group G under the assumption that some subgroups of prime power orders belong to （G）.