摘要
利用Sylow p-子群的极大子群的m-嵌入性质研究群G的p-模子群O^p(G),并得到G的主因子结构.主要证明了如下结果:1)若G的Sylow p-子群的每个极大子群在G中是m-嵌入的,则G是p-超可解的或Op(G)=G;2)设E■G,若E的Sylow p-子群的每个极大子群在G中是m-嵌入的,且O^p(G)<G,则|E_p|=p或E之下的每一个G-主因子A/B均满足下列情形之一:(1)A/B≤ΦG(/B);(2)A/B是p′-群;(3)|A/B|=p.
In this paper,the influence of m-embedded subgroups on the structure of p-modular subgroups is discussed and the structure of chief factors of G is obtained.The following results are mainly shown:1)If every maximal subgroup of Sylow p-subgroup of G is m-embedded in G,then G is p-supersolvable or O^p(G)=G;2)Let E■G,if every maximal subgroup of Sylow p-subgroup of E is m-embedded in G and O^p(G)<G,then|E_p|=por every G-chief factor A/B below E satisfies one of the following conditions:(1) A/B≤Φ(G/B);(2) A/Bis a p′-group;(3) |A/B|=p.
出处
《扬州大学学报（自然科学版）》
CAS
北大核心
2017年第3期1-3,8,共4页
Journal of Yangzhou University：Natural Science Edition
基金
国家自然科学基金资助项目(11271016)
伊犁师范学院科研重点项目(2016YSZD06)
关键词
m-嵌入子群
p-模子群
P-超可解群
主因子
m-embedded subgroup
p-modular subgroup
p-supersolvable group
chief factor
作者简介
联系人,E-mail：dqgbj2008@163.com.
