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弱s-置换子群与有限群的p-幂零性
  • ISSN号：1000-5471
  • 期刊名称：西南师范大学学报(自然科学版)
  • 时间：2012.2.20
  • 页码：8-11
  • 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（11171243）
  • 相关项目：有限群的数量性质与子群的广义正规性
作者： 陈云坤|黎先华|
关键词： 弱-可补, P-幂零群, 极小子群, weakly g-supplemented, p-nilpotent group, minimal subgroup
中文摘要：

设H是有限群G的子群,称H为弱-可补的,如果存在G的子群T使得G=HT且H∩T≤,其中HG是由H所有在G中s-半置换子群生成的群.设G是有限群,p｜｜G｜.如果下列①和②之一成立,则G为p-幂零群：①（｜G｜,p-1）=1,G有Sylowp-子群P使得P的每个极小子群在G中弱-可补,且p=2时P与四元数群无关;②G是与A4无关的群,p=minπ（G）,N G使得G/N是p-幂零群,N的一个Sylowp-子群P的每个p2阶子群都是G的弱-可补子群.

英文摘要：

Let H be a subgroup of a finite group G. H is called weakly s-supplemented if there exists a subgroup T of G such that G=TH and H ∩T≤H2G, where H2G is the subgroup generalized by all subgroups of H which are s-semipermutable in G. Let G be a finite group and pen（ ｜G｜ ）. If one of the following （1） and （2） holds, then G is p-nilpotent ： （1） （ ｜ G ｜ , P- 1） = 1, G has a Sylow p-subgroup P such that every minimal subgroup of P is weakly g-supplemented in G, moreover if p=2, then P is A4-free; （2） G is A4-free, p=min π（G）, N〈1G such that G/N is p-nilpotent, every subgroup of order p2 in every Sylow p-subgroup P of N is weakly s-supplemented in G.

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期刊信息
  • 《西南师范大学学报：自然科学版》
  • 北大核心期刊（2011版）
  • 主管单位:中华人民共和国教育部
  • 主办单位:西南大学
  • 主编：李明
  • 地址：重庆市北碚区天生路2号
  • 邮编：400715
  • 邮箱：xhtang@swu.cn
  • 电话：023-68252540
  • 国际标准刊号：ISSN：1000-5471
  • 国内统一刊号：ISSN：50-1045/N
  • 邮发代号:78-22
  • 获奖情况:
  • 全国高校优秀学报,重庆市十佳科技期刊,重庆市一级期刊
  • 国内外数据库收录:
  • 美国化学文摘（网络版）,美国数学评论（网络版）,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:17791