∑~*-嵌入子群对有限群的可解性的影响  

Influence of Σ~*-embedded subgroups on solvability of finite groups

作　　者：贺玉[1] 郭秀云[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2014年第1期78-85,共8页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11071155);上海市教育委员会重点学科建设资助项目(J50101)

摘　　要：设H是有限群G的子群, K/L是G的任一非Frattini主因子.如果对每一满足L≤A＜B≤K且A是B的极大子群的子群对（A,B）,都有HA=HB或者H∩A=H∩B,则称H是G的∑＊-嵌入子群.通过有限群G的某些子群的∑＊-嵌入性,给出了一些有限群G的正规子群为可解群的一些判别条件,推广了已有的一些结论.Let H be a subgroup of a finite group G and K/L be a non-Frattini chief factor of G. If HA = HB or H∩A=H∩B for each pair （A,B） with A a maximal subgroup of B and L≤A〈B≤K, then H is said to be a E＊- embedded subgroup of G. Some new criteria for a normal subgroup in a finite group to be solvable are obtained based on the assumption that some subgroups are E＊-embedded subgroups of G and some known results are generalized.

关 键 词：Frattini主因子 可解群 覆盖远离性质 

分 类 号：O152.1[理学—数学]