π-闭-Sylow塔群的一些必要条件  

Prerequisites of π-closed-Sylow-tower Groups

作　　者：於遒[1] 查明明[1] 李保军[2] 

机构地区：[1]淮海工学院东港学院基础系 [2]徐州师范大学数学系

出　　处：《淮阴工学院学报》2005年第3期10-12,共3页Journal of Huaiyin Institute of Technology

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塔群的性质的基础上,利用极大子群、s-正规子群等,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:(1)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。(2)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-正规,则G为可解群。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. Discussion is made on the properties of π-closed-Sylow-tower group as follows through the use of maximal subgroups and s-normal subgroups: Let G be a π-closed-Sylow-tower group, (1) If the index of every maximal subgroup containing Hall π'- subgroup is a prime, then G is π-supersolvable. (2) If every primary subgroup contained in π'-Hall subgroup is -normal in G, then G is solvable.

关 键 词：Π-闭-SYLOW塔群 极大子群 S-正规子群 π-超可解群 可解群 

分 类 号：O152.1[理学—数学]