某些子群为HC-子群的有限群

Finite groups in which some subgroups are HC-subgroup

群G的一个子群H称为G的HC-子群,如果存在一个G的正规子群T,使得G=HT并且H^g∩N_T(H)≤日对任意g∈G都成立.文章研究了p^2阶子群以及一般的p^k阶子群为HC-子群时有限群G的结构.给出了有限群为p-幂零群以及超可解群的一些条件.

A subgroup H of a group G is called an 7-/C-subgroup of G if there exists a normal subgroup T of G such that G = HT and H9 N NT（H） ≤ H for all g E G. In this paper, we investigate the structure of a finite group G under the assumption that certain subgroups of the prime power order are HC-subgroups in G. Some conditions for a finite group to be p-nilpotent and supersolvable are given. For example, we prove that if all subgroups of G of order p^2 are T/C-subgroup in G, then G is p-nilpotent.