有限群的弱Φ-可补子群与超可解性  

Weakly Φ-supplemented Supgroups and Supersolvability of Finite Groups

作　　者：邱招丰[1] 

机构地区：[1]温州职业技术学院,浙江温州325035

出　　处：《杭州师范大学学报（自然科学版）》2013年第6期513-516,共4页Journal of Hangzhou Normal University(Natural Science Edition)

摘　　要：群G的一个子群H称为在G中弱Φ-可补,如果存在G的一个次正规子群K,使得G=HK且H∩K≤Φ(H),其中Φ(H)为子群H的Frattini子群.文章利用子群的弱Φ-可补性对有限群结构的影响,给出了有限群为超可解群的若干充分条件.A subgroup H of group G is called weakly φ-supplemented in G, if there is a subnormal subgroup K of G, such that G= HK and H ∩K≤φ（H）, where φ（H） is the Frattini subgroup of H. Using the effects of weakly φ-supplemented feature of subgroups on the structure of finite groups, the paper obtained some sufficient conditions for that finite groups were supersolvable groups.

关 键 词：弱Φ-可补子群 FRATTINI子群 超可解群 极大子群 

分 类 号：O152.1[理学—数学]