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∑*-嵌入子群对有限群的可解性的影响
引用本文:贺玉,郭秀云.∑*-嵌入子群对有限群的可解性的影响[J].应用数学与计算数学学报,2014(1):78-85.
作者姓名:贺玉  郭秀云
作者单位:上海大学理学院
基金项目: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.

关 键 词:Frattini主因子  可解群  覆盖远离性质

Influence of ∑*-embedded subgroups on solvability of finite groups
HE Yu;GUO Xiu-yun.Influence of ∑*-embedded subgroups on solvability of finite groups[J].Communication on Applied Mathematics and Computation,2014(1):78-85.
Authors:HE Yu;GUO Xiu-yun
Institution:HE Yu;GUO Xiu-yun;College of Sciences,Shanghai University;
Abstract: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.
Keywords:Frattini chief factor  solvable group  cover-avoiding property
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