含有C＊-正规子群的有限群  

Finite Groups with Some C＊-normal Subgroups

作　　者：何宣丽[1] 李样明[2] 王燕鸣[3] 

机构地区：[1]中山大学数计学院,广东广州510275 [2]广东教育学院数学系,广东广州510310 [3]中山大学//岭南学院数计学院,广东广州510275

出　　处：《中山大学学报（自然科学版）》2009年第5期12-15,23,共5页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(10871210);广东省自然科学基金资助项目(06023728)

摘　　要：设G为有限群,H是G的子群。称H是G的S-拟正规子群,如果对G的任意Sylow子群P,有HP=PH;称H是G的S-拟正规嵌入子群,若H的Sylow子群为G的某个S-拟正规子群的Sylow子群;称H是G的C*-正规子群,如果G有正规子群K使得G=HK且满足H∩K在G中是S-拟正规嵌入的。设d是p-群P的最小生成元个数。考虑P的d个极大子群构成的集合Μd(P)=P1,…,Pd且使得它们的交是P的Frattini子群Φ(P)。对Μd(P)中的群在满足C*-正规假设条件下群的结构进行了研究,并推广了最近的一些结论。Let G be a finite group and H a subgroup of G. It says that H is an S -quasinormal subgroup of G if HP = PH for any Sylow subgroup P of G ; H is an S -quasinormally embedded subgroup of G if every Sylow subgroup of H is a Sylow subgroup of some S -quasinormal subgroup of G ; H is a C＊-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H n K is S -quasinormally embedded in G. Let d be the smallest generator number of a p -group P. Consider a set Md （P） = { P1 ,…, Pd } of maximal subgroups of P such that ∩i=1^dPi= φ（P） . The aim is to investigate the structure of finite group G under the assumption that all members in Md（P） are C＊-normal in G , and generalizes some recent results.

关 键 词：C＊-正规子群 S-拟正规嵌入子群 P-幂零群 

分 类 号：O15[理学—数学]