| 半覆盖-远离及X-半置换子群与有限群的p-幂零性 |
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| 引用本文： | 石向东,韦华全,周宇珍. 半覆盖-远离及X-半置换子群与有限群的p-幂零性[J]. 广西民族大学学报, 2012, 0(1): 63-67 |
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| 作者姓名： | 石向东 韦华全 周宇珍 |
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| 作者单位： | [1]梧州学院数理系,广西梧州543002 [2]广西师范学院数学科学学院,广西南宁530001 [3]广西师范学院继续教育学院,广西南宁530001 |
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| 基金项目： | 国家自然科学基金（10961007,10871210）; 广西自然科学基金（0991101）; 广西教育厅科研基金 |
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| 摘 要： | 设H是有限群G的正规子群使得G/H为p-幂零群,P是H的一个Sylowp-子群.若NG（P）为p-幂零群且下列条件之一成立,则G是p-幂零群：（1）P的极大子群在G中半覆盖-远离或Fp（H）-半置换;（2）P的二次极大子群在G中半覆盖-远离或Fp（H）-半置换.
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| 关 键 词： | 有限群 p-幂零群 半覆盖-远离子群 X-置换 极大子群 |
Semi-cover-avoiding and X-semipermutable Subgroups and the p-nilpotency of Finite Groups |
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| SHI Xiang-dong,WEI Hua-quan,ZHOU Yu-zhen. Semi-cover-avoiding and X-semipermutable Subgroups and the p-nilpotency of Finite Groups[J]. Journal of Guangxi University For Nationalities(Natural Science Edition), 2012, 0(1): 63-67 |
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| Authors: | SHI Xiang-dong WEI Hua-quan ZHOU Yu-zhen |
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| Affiliation: | 1.Department of Mathematics and Physics,Wuzhou College,Wuzhou 543002,China; 2.School of Mathematics Science,Guangxi Teacher＇s Education University,Nanning 530001,China; 3.School of Continuing Education,Guangxi Teacher＇s Education University,Nanning 530001,China) |
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| Abstract: | Let H be a normal subgroup of a finite group G such that G/H is p-nilpotent and let P be a Sylow p-subgroup of H.If NG（P） is p-nilpotent and one of the following holds,then G is p-nilpotent：（1） Every maximal subgroup of P is either semi-cover-avoiding or Fp（H）-semipermutable in G;（2） Every 2-maximal subgroup of P is either semi-cover-avoiding or Fp（H）-semipermutable in G. |
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| Keywords: | finite group p-nilpotent group semi-cover-avoiding subgroup X-semipermutable subgroup maximal subgroup |
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