几乎s-嵌入子群与有限群的p-幂零性

Nearly s-Embedded Subgroups and the p-Nilpotency of Finite Groups

设G为有限群且H为G的子群.H称为在G中拟s-正规,如果H与G的所有Sylow子群可交换.称H在G中为s-半置换,如果对任意G的Sylowp-子群P,有HP=PH,其中p∈π(G)且(|H|,p)=1.称G的子群H为在G中几乎s-嵌入,如果存在G的s-拟正规子群T使得HsG=HT且H∩T≤HssG,其中HssG为G的包含于H的s-半置换子群.该文研究Sylow子群的极大子群的局部几乎s-嵌入性对有限群p-幂零性的影响.

Let Gbe a finite group and Ha subgroup of G.His said to be s-permutable in Gif H permutes with every Sylow subgroup of G.His said to be s-semipermutable in Gif for any Sylowp-subgroup P of G,HP =PH,whenever p ∈π(G)and(|H|,p)=1.His said to be nearly s-embedded in Gif there exists ans-permutable subgroup T of Gsuch that G =HTand H ∩T  HssG,where HssGis ans-semipermutable subgroup of Gcontained in H.This paper investigates the influence of the local nearly s-embedding of maximal subgroups of Sylow subgroups on the p-nilpotency of finite groups.