有限群的CAP-拟正规子群（英文）  

On CAP-quasinormal Subgroups of Finite Groups

作　　者：张丽[1] 吴珍凤 郭文彬[1] 

机构地区：[1]中国科学技术大学数学科学学院,合肥安徽230026

出　　处：《数学进展》2017年第6期897-907,共11页Advances in Mathematics（China）

基　　金：supported by NSFC(No.11771409);Wu Wen-Tsun Key Laboratory of Mathematics of Chinese Academy of Sciences

摘　　要：有限群G的一个子群A称为G的广义CAP-子群,如果对于任一G-主因子H/K,要么A避免H/K,要么下述成立:(1)如果H/K非交换,那么(A∩H)K/K是H/K的一个Hall子群;(2)如果H/K是一个p-群,那么|G:N_G((A∩H)K)|是一个p-数.G的一个子群H称为在G中是CAP-拟正规的,如果G有一个拟正规子群T和一个广义CAP-子群A满足HT在G中是S-拟正规的并且H∩T≤A≤H.本文得到了CAP-拟正规子群的一些结果并用它们给出一个有限群属于某个包含超可解群的饱和群系的条件.文章推广了很多最近的结果.A subgroup A of a finite group G is called a generalized CAP-subgroup of G if for each G-chief factor H/K either A avoids H/K or the following hold： （1） if H/K is non-abelian, then （An H）K/K is a Hall subgroup of H/K; （2） if H/K is a p-group, then ｜G ： NG（（A ∩H）K）｜ is a p-number, We say that a subgroup H of G is CAP-quasinormal in G if G has a quasinormal subgroup T and a generalized CAP-subgroup A such that HT is S-quasinormal in G and H∩T ≤A ≤H. In this paper, we obtain some results about the CAP- quasinormal subgroups and use them to give the condition under which a finite group belongs to a saturated formation containing supersolvable groups. Many recent results are extended.

关 键 词：有限群 CAP一拟正规子群 饱和群系 F-超中心p-幂零群 

分 类 号：O152.1[理学—数学]