■-可补子群对有限群结构的影响  

Influence of ■-Supplemented Subgroups on the Structure of Finite Group

作　　者：唐娜[1,2] 黎先华[2] 

机构地区：[1]淮阴师范学院数学科学学院,江苏淮安223300 [2]苏州大学数学科学学院,江苏苏州215006

出　　处：《吉林大学学报（理学版）》2014年第2期266-268,共3页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11171243);国家自然科学基金天元基金(批准号:11226285)

摘　　要：利用■-可补子群研究p-超可解群,得到了两个主要结果:1)令G是p-可解的且p G,则G是p-超可解的当且仅当Fp(G)中包含Op′(G)的所有极大子群在G中■-可补,这里■是所有p-超可解群组成的群类;2)令G是p-可解的且p G,则G是p-超可解的当且仅当Fp(G)的非循环Sylowp-子群的极大子群在G中■-可补,这里■是包含所有p-超可解群组成的群类.We took the advantage of F-supplemented subgroups to study the structure of p-supersolvable groups and obtained two main results.1）Let G be p-solvable and p｜｜G｜ ,then G is p-supersolvable if and only if every maximal subgroup of Fp （G）containing O p′（G）is F-supplemented in G,where F is the class of all p-supersolvable groups.2）Let G be p-solvable and p｜｜G｜ ,then G is p-supersolvable if and only if every maximal subgroup of non-cyclic Sylow p-subgroups of Fp （G）is F-supplemented in G,where F is the class of all p-supersolvable groups.

关 键 词：F-可补子群 P-超可解群 饱和群系 FITTING子群 

分 类 号：O152.1[理学—数学]