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最高阶元素个数为4p~2的有限群是可解群
  • ISSN号：1000-2367
  • 期刊名称：河南师范大学学报(自然科学版)
  • 时间：2012.7.15
  • 页码：5-8
  • 分类：O152.1[理学—数学;理学—基础数学]
  • 作者机构：[1]西南大学数学与统计学院,重庆400715, [2]重庆第二师范学院数学与信息工程系,重庆400067
  • 相关基金：国家自然科学基金（11171364）; 重庆市科委自然科学基金（cstc2011jjA1495）; 重庆市教委资助项目（KJ110609）
  • 相关项目：有限群的算术性质和单群的刻画
作者： 晏燕雄|YAN Yan-xiong1,2(1.School of Mathematics and Finan|2.Deparment of Mathematics and Information Enginee|
关键词： 有限群, 可解群, 元素的阶, m-型, finite groups, solvable groups, the order of elements, m-type
中文摘要：

研究了最高阶元素个数对有限群结构的影响.运用群阶的素因子,k阶循环子群共轭类的长,以及K3-单群和K4-单群的有关结论,证明了最高阶元素个数为｜M（G）｜=4p2的有限群G是可解群,其中p是素数.

英文摘要：

Affection on the structure of finite group as the number of maximal order elements is discussed. It is proved that such finite groups with 4p2 maximal order elements are solvable by making use of corresponding results on K3-simple groups and K4-simple groups, as well as the prime factor of the order of a finite group and the length of the conjugate class of cyclic subgroups with order k, where p is a prime

同期刊论文项目
有限群的算术性质和单群的刻画
期刊论文 76 会议论文 1
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期刊信息
  • 《河南师范大学学报：自然科学版》
  • 北大核心期刊（2011版）
  • 主管单位:河南师范大学
  • 主办单位:河南师范大学
  • 主编：王记录
  • 地址：河南省新乡市建设东路46号
  • 邮编：453007
  • 邮箱：
  • 电话：0373-3329394 3329272
  • 国际标准刊号：ISSN：1000-2367
  • 国内统一刊号：ISSN：41-1109/N
  • 邮发代号:36-55
  • 获奖情况:
  • 国家新闻出版局、国家科委优秀学报奖,河南省科委、河南省教委优秀学报
  • 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）,英国农业与生物科学研究中心文摘,德国数学文摘,英国动物学记录,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）
  • 被引量:7535