有限群的ss-置换子群  

On ss-permutable subgroups of finite groups

作　　者：卢家宽[1] 郭秀云[2] 

机构地区：[1]广西师范大学数学科学学院,广西桂林541004 [2]上海大学数学系,上海200444

出　　处：《纯粹数学与应用数学》2010年第4期587-596,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(10771132);SGRC(G2310);上海市教委重点学科建设项目(J50101)

摘　　要：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.

关 键 词：ss-置换子群 s-置换子群 超可解群 

分 类 号：O152.1[理学—数学]