关于ss-拟正规子群和c-正规子群

On ss-quassinormal subgroups and c-normal subgroups

设G是有限群,H是G的子群.称H在G中ss-拟正规,如果H存在1个补子群B,满足H和B的每个Sylow子群可以交换.称H在G中c-正规,如果存在G的正规子群K,使得G=HK且H∩K≤H_G,这里H_G是H在G中的正规核.同时考虑这2个概念,并应用群论研究的"或"思想方法,得出的主要结论是:当p是满足|G|的素因子且■是G的1个Sylow p-子群,如果P的极大子群在G中c-正规,或在G中ss-拟正规时,群G是p-幂零群.

Let G be a finite group, H is a subgroup of G . A subgroup H is said to be an ss-quassinormal subgroup of G , if there is a supplement B of H to G such that H permutes with every Sylow subgroup of B . However, A subgroup H of G is called c-normal in G provided that there exists a normal subgroup K such as G=HK and H∩K≤H G, where H G is the normal core of H in G . The two concepts are considered in a group at the same time, and we apply the “or” method of group theory to the research. It concludes as follows: suppose p a prime dividing |G| with (|G|,p-1)=1 and let P be a Sylow p -subgroup of a group G , and if every maximal subgroup of P is either ss -quassinormal or c -normal, then G is p -nilpotent.