弱H-子群对有限群结构的影响

Influence of Weakly H-subgroups on the Structure of Finite Groups

设G为有限群,称H为G的一个H-子群,若对所有g∈G,使得NG(H)∩Hg≤H成立;称H为G的一个弱H-子群,若存在G的一个正规子群K,使得G=HK且H∩K为G的H-子群.该文研究弱H-子群对有限群结构的影响,推广了最近的一些结论.

Let G be a finite group. A subgroup of H is called an -subgroup in G if NG（H） 0 Hg≤H for all g E G. A subgroup H of G is called a weakly -subgroup in G if there exists a normal subgroup K of G such that G----HK and H [-]K is an -subgroup in G.We investigate the influence of weakly -subgroups on the structure of finite groups. Some recent results are generalized.