有限群的π-闭-Sylow塔群的性质  

Properties of π-closed-Sylow-tower Groups

作　　者：於遒[1] 查明明[2] 李保军[3] 

机构地区：[1]淮海工学院东港学院基础部,江苏连云港222069 [2]淮海工学院数理科学系,江苏连云港222005 [3]徐州师范大学数学系,江苏徐州220006

出　　处：《淮海工学院学报（自然科学版）》2005年第2期4-6,共3页Journal of Huaihai Institute of Technology:Natural Sciences Edition

基　　金：国家自然科学基金资助项目(10171086)

摘　　要：称群G为π闭Sylow塔群,若群G存在正规Hallπ子群为Sylow塔群.在π闭Sylow塔群性质的基础上,利用极大子群、s可补子群等,给出了一个π闭Sylow塔群为π超可解群、可解群的一些条件.主要结论:若G为π闭Sylow塔群,且G的包含Hallπ′子群的极大子群在G中的指数为素数,则G为π超可解群;G为π闭Sylow塔群,若G中任一Hallπ′子群的素数幂阶子群在G中s可补,则G为可解群.A group G is called a π-closed-Sylow-tower group if there exists a normal Hall π-subgroup in G, which is a Sylow-tower group. This paper deals with the properties of π-closed-Sylow-tower group through the use of maximal subgroups and s-supplemented subgroups. It arrives at the following conclusions: let G be a π-closed-Sylow-tower group, G is π-supersolvable if the index of every maximal subgroup M containing Hall-π′ subgroup is a prime; G is solvable if every primary subgroup contained in π′-Hall subgroup is s-supplemented in G.

关 键 词：Π-闭-SYLOW塔群 极大子群 s-可补 π-超可解群 可解群 

分 类 号：O152.1[理学—数学]