子群的m-嵌入性質對p-模子群結構的影響
發(fā)布時間：2018-08-03 08:03
【摘要】：利用Sylow p-子群的極大子群的m-嵌入性質研究群G的p-模子群O~p(G),并得到G的主因子結構.主要證明了如下結果:1)若G的Sylow p-子群的每個極大子群在G中是m-嵌入的,則G是p-超可解的或Op(G)=G;2)設E■G,若E的Sylow p-子群的每個極大子群在G中是m-嵌入的,且O~p(G)G,則|E_p|=p或E之下的每一個G-主因子A/B均滿足下列情形之一:(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，
本文編號：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，
本文編號：2161119
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