有限群的超可解与幂零性质(英文)

Supersolubility and nilpotency of finite groups

设H是有限群G的一个子群,若存在子群B使得HB=G且H与B的每个Sylow都可换,则称H在G中SS-拟正规。如果存在G的正规子群T使得HT在G中s-可换,H∩T在G中SS-拟正规,则称H为G的弱SS-拟正规子群。文中研究了某些弱SS-拟正规子群对有限群结构的影响。一系列原有的结论得到了统一和推广。

Suppose that H is a subgroup of a finite group G and that there exists a subgroup B. If HB=G and H is per-mutable with every Sylow subgroup of B,H is SS-quasinormal in G. Suppose that there exists a normal subgroup T of G and that HT is s-permutable. If H∩T is SS-quasinormal in G,H is a weakly SS-quasinormal subgroup of G. In this pa-per, we have investigated the influence of some weakly SS-quasinormal subgroups on the structure of finite groups. A se-ries of known results in the literature are unified and generalized.