有限群的ss-置换子群

On ss-permutable subgroups of finite groups

设G为有限群,称G的子群H为ss-置换子群,如果存在G的次正规子群B使得G=HB,且H与B的任意Sylow子群可以交换,即对任意X∈Syl(B)有XH=HX.利用子群的ss-置换性来研究有限群的结构,得到有限群超可解的两个充分条件.

A subgroup H of a finite group G is called to be ss-permutable in G if G has a subnormal subgroup B such that HB = G and HS = SH for any Sylow subgroup S of B.We fix in every non-cyclic Sylow subgroup P of G a subgroup D satisfying 1 ｜D｜ ｜P｜ and study the structure of G under the assumption that all subgroups H with ｜H｜ = ｜D｜ are ss-permutable in G.