子群的m-嵌入性质对p-模子群结构的影响
发布时间：2018-08-03 08:03
【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.
[Abstract]:By using the m- embedding property of maximal subgroups of Sylow p- subgroups, we study the p-module subgroups of G and obtain the principal factorial substructure of G. This paper mainly proves the following result: 1) if every maximal subgroup of Sylow p- subgroup of G is m- embedded in G, then G is p- supersolvable or Op (G) / G ~ 2) Let E be if every maximal subgroup of Sylow p- subgroup of E is m- embedded in G. And Ospp (G) G, satisfies one of the following cases: (1) A / B 鈮，
本文编号：2161119
[Abstract]:By using the m- embedding property of maximal subgroups of Sylow p- subgroups, we study the p-module subgroups of G and obtain the principal factorial substructure of G. This paper mainly proves the following result: 1) if every maximal subgroup of Sylow p- subgroup of G is m- embedded in G, then G is p- supersolvable or Op (G) / G ~ 2) Let E be if every maximal subgroup of Sylow p- subgroup of E is m- embedded in G. And Ospp (G) G, satisfies one of the following cases: (1) A / B 鈮，
本文编号：2161119
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