| 有限群的正规嵌入子群 |
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| 引用本文： | 郭鹏飞,魏先彪.有限群的正规嵌入子群[J].上海大学学报(自然科学版),2009,15(5):496-500. |
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| 作者姓名： | 郭鹏飞 魏先彪 |
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| 作者单位： | 1.上海大学 理学院,上海 200444; 2.连云港师范高等专科学校 数学系,江苏 连云港 222006 |
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| 基金项目： | 国家自然科学基金资助项目，江苏省高校"青蓝工程"资助项目 |
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| 摘 要： | 群G的子群H称为G的正规嵌入子群, 如果对于|H|的每个素因子p, 存在G的一个正规子群K,使得H的一个Sylow p-子群也是K的一个Sylow p-子群. 假设对于G的每个非循环Sylow子群P有一个子群D,使得1<|D|<|P|,且P的所有阶为|D|和2|D|(若P是非交换2-群且|P:D|>2)的子群H是G的正规嵌入子群, 得到G为p-幂零群以及超可解群的一些充分条件, 部分结果被推广到群系.
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| 关 键 词： | 正规嵌入子群 p-正规嵌入子群 p-幂零群 超可解群 |
| 收稿时间： | 2008-05-12 |
Normally Embedded Subgroups of Finite Groups |
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| GUO Peng-Fei,WEI Xian-Biao.Normally Embedded Subgroups of Finite Groups[J].Journal of Shanghai University(Natural Science),2009,15(5):496-500. |
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| Authors: | GUO Peng-Fei WEI Xian-Biao |
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| Affiliation: | 1.College of Sciences, Shanghai University, Shanghai 200444, China; 2.Department of Mathematics, Lianyungang Teachers College, Lianyungang 222006, Jiangsu, China |
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| Abstract: | A subgroup H of a finite group G is said to be normally embedded in G if,for every prime p dividing the order of H,there exists a normal subgroup K of G such that a Sylow p-subgroup of H is also a Sylow p-subgroup of K.This paper assumes that every non-cyclic Sylow subgroup P of G has a subgroup D such that 1 <|D|<|P| and all subgroups H of P with order |H| = |D| and with 2|D| ( if P is a non-abelian 2-group and |P:D|>2) are normally embedded in G,and some sufficient conditions are obtained on G to be p-nilpotent groups and supersolvable groups.Moreover,some of them are extended to formations. |
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| Keywords: | normally embedded subgroups p-normally embedded subgroups p-nilpotent groups supersolvable groups |
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