| 关于CAP-子群的一点注记（英文） |
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| 引用本文： | 金卫雄,魏先彪.关于CAP-子群的一点注记（英文）[J].大学数学,2011,27(5):12-15. |
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| 作者姓名： | 金卫雄 魏先彪 |
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| 作者单位： | 1. 连云港师范高等专科学校数学系,江苏连云港,222006
2. 安徽建筑工业学院数理系,安徽合肥,230022 |
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| 基金项目： | The National Natural Science Foundation of China(10771132);SGRC(GZ310) |
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| 摘 要： | 对于有限群G的每一主因子H/K来说,若G的子群L满足LH=LK或者L∩H=L∩K,则称L是G的CAP-子群.本文通过假设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CAP-子群,得到G为p-幂零群的一个结果.
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| 关 键 词： | CAP-子群 p-幂零群 超可解群 饱和群系 |
A Note on CAP-Subgroups of Finite Groups |
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| JIN Wei-xiong,WEI Xian-biao.A Note on CAP-Subgroups of Finite Groups[J].College Mathematics,2011,27(5):12-15. |
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| Authors: | JIN Wei-xiong WEI Xian-biao |
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| Institution: | JIN Wei-xiong1,WEI Xian-biao2(1.Department of Mathematics,Lianyungang Teachers College,Lianyungang,Jiangsu 222006,China,2.Department of Mathematics,Anhui University of Architecture,Hefei,Anhui 230022,China) |
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| Abstract: | We call a subgroup U of a finite group G a CAP-subgroup of G if for every chief factor H/K of G, we have UH =UK or U H=U K. In this paper, we investigate 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 CAP-subgroups of G, and give a characterization for a group G to be p-nilpotent. |
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| Keywords: | CAP-subgroups p-nilpotent groups supersolvable groups saturated formations |
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