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恰有两个子群共轭类长的有限群
  • 期刊名称：数学学报
  • 时间：0
  • 页码：619-622
  • 语言：中文
  • 分类：O152.1[理学—数学;理学—基础数学]
  • 作者机构：[1]贵州师范大学数学与计算机科学学院,贵阳550001
  • 相关基金：国家自然科学基金资助项目（10871032）; 贵州省科学技术基金资助项目（黔科合J字LKS（2010）04）
  • 相关项目：有限群的特征标理论及相关共轭不变量
作者： 唐锋|
关键词： SYLOW子群, 弱s-置换子群, 次正规子群, 正规化子, P-幂零群, Sylow subgroup, weakly s-permutable subgroup, subnormal subgroup, normalizer, {p-nilpotent} group
中文摘要：

利用Sylow子群的极大子群在其所在的Sylow子群正规化子中的弱s-置换性得到有限群的p-幂零性的一些刻画.证明了：设G为有限群,p为｜G｜的素因子,且（｜G｜,p-1）=1,P∈Sylp（G）;若P的每个极大子群在NG（P）中弱s-置换且P′在G中s-置换,则G为p-幂零群.同时得到几个有关群系的结论.

英文摘要：

In this paper,using the condition that the maximal subgroups of a given Sylow p-subgroup of G are weakly s-permutable in their normalizer,some characterizations about the p-nilpotency of G are obtained.The following result is proved.Let p be a prime divisor of ｜G｜ with（｜G｜,{p-1}）=1,P∈Sylp（G）.If every maximal subgroup of P is weakly s-permutable in NG（P） and P′ is s-permutable in G,then G is p-nilpotent.Some results about formation are also obtained.

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