| Sylow子群及其极大子群对有限群结构的影响 |
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| 引用本文： | 胡玉生,张利英.Sylow子群及其极大子群对有限群结构的影响[J].北京联合大学学报(自然科学版),2012,26(1):70-72. |
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| 作者姓名： | 胡玉生 张利英 |
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| 作者单位： | 安徽财经大学统计与应用数学学院,安徽蚌埠,233030;安徽财经大学统计与应用数学学院,安徽蚌埠,233030 |
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| 基金项目： | 安徽财经大学校级科研项目(ACKYQ1152ZC);安徽省高校人文社科项目(2011SK166);安徽省高校人文社科项目(2011SK177) |
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| 摘 要： | 利用Sylow子群及其极大子群在有限群G中完全条件置换得出了G超可解的结论,并把结果推广到群系中,得到了包含超可解群类的饱和群系的充分条件,推广了一些已知结果。
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| 关 键 词： | 完全条件置换子群 Sylow子群 极大子群 超可解群 |
The Influence of Sylow Subgroups and Its Maximal Subgroups on the Finite Groups |
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| HU Yu-sheng,ZHANG Li-ying.The Influence of Sylow Subgroups and Its Maximal Subgroups on the Finite Groups[J].Journal of Beijing Union University,2012,26(1):70-72. |
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| Authors: | HU Yu-sheng ZHANG Li-ying |
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| Institution: | (Institute of Statistics and Applied Mathematics,Anhui Financial University,Bengbu Anhui 233030,China) |
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| Abstract: | By using the completely conditional permutability of the Sylow subgroups and its maximal subgroups of finite group G,the sufficient conditions for a finite group G to be supersolvable are proved and the results are generalized to formations.Moreover,the sufficient condition for a saturated formation containing the class of all finite supersolvable groups is also obtained,and some known results are generalized. |
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| Keywords: | Completely conditionally permutable subgroup Sylow subgroup Maximal subgroup Supersolvable group |
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