| 有限群的正规p-补的一些结论 |
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| 引用本文： | 陈德勤.有限群的正规p-补的一些结论[J].四川理工学院学报(自然科学版),2011,24(3):275-277. |
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| 作者姓名： | 陈德勤 |
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| 作者单位： | 四川理工学院理学院,四川自贡,643000 |
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| 基金项目： | 四川理工学院科研基金，四川理工学院教改项目 |
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| 摘 要： | 有限群的极小子群在群论研究中有很重要的地位。文章探讨极小子群对有限群的p-幂零性,并得到:设P是群G的Sylowp-子群,满足Ω1(P∩F(G))≤Z∞(G),如果NG(Z(P))有一个正规p-补,那么G有一个正规p-补;若G还没有与A4同构的主因子,则G有一个正规p-补。
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| 关 键 词： | 幂零性 p-幂零的 正规子群 |
Some Results on p-nilpotence of Finite Groups |
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| CHEN De-qin.Some Results on p-nilpotence of Finite Groups[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,2011,24(3):275-277. |
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| Authors: | CHEN De-qin |
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| Institution: | CHEN De-qin (School of Science,Sichuan University of Science & Engineering,Zigong 643000,China) |
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| Abstract: | It is very important for minimal subgroups of groups in the research of groups.In this paper,we will give some results on the influence of minimal subgroup on the structure of p-nilpotence.And a main result is gotten: If P is a Sylow p-subgroups of G,suppose that Ω1(P∩F(G))≤Z∞(G),and NG(Z(P)) has a normal p-complement,then G has a normal p-complement.And if G has no main factor,which is isomorphic with A4,then G has a sylow p-subgroups. |
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| Keywords: | nilpotence p-nilpotent normal subgroups |
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