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子群的半覆盖-避开性与有限群的结构
  • ISSN号：0583-1431
  • 期刊名称：《数学学报》
  • 时间：0
  • 分类：O152[理学—数学;理学—基础数学]
  • 作者机构：[1]苏州大学数学科学学院,苏州215006
  • 相关基金：国家自然科学基金资助项目（10571128）;苏州市高层次人才项目资助项目
作者： 黎先华[1], 杨元韡[1]
关键词： 解群, 半CAP-子群, P-幂零性, 群系, semi CAP-subgroup, solvability, p-nilpotency, formation
中文摘要：

设G是有限群，H为G的子群．如果存在一个主群列1=G0△G1△……Gn-1△Gn=G1使得对每个i=1，2，…，n，或者H覆盖Gi／Gi-1，或者H避开Gi／Gi-1，则称H为G的半覆盖避开子群．利用G的Sylow子群的极大子群，Sylow子群的2-极大子群的半覆盖-避开性得到了群的可解性，P-幂零性的判别，同时得到了群系的一些结论．

英文摘要：

Let G be a finite group. A subgroup H of G is said to be a semi CAP- subgroup of G if there exists a given chief series 1 = G0△G1△……Gn-1△Gn=G such that for every i = 1, 2,..., n, either H covers Gi/Gi-1 or H avoids Gi/Gi-1. In this paper, using the condition that some maximal subgroups or 2-maximal subgroups are semi CAP-subgroups of G, we get some criterions for solvability, and p-nilpotency of G. Meanwhile, we obtain some results about formation.

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期刊信息
  • 《数学学报》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国科学院数学与系统科学研究院数学研究院
  • 主编：李炳仁
  • 地址：北京市海淀区中关村东路55号
  • 邮编：100080
  • 邮箱：Actamath@amss.ac.cn
  • 电话：010-62551910
  • 国际标准刊号：ISSN：0583-1431
  • 国内统一刊号：ISSN：11-2038/O1
  • 邮发代号:2-502
  • 获奖情况:
  • 1996年中科院优秀科技期刊二等奖,1997年全国优秀科技期刊二等奖,2000年中科院优秀科技期刊二等奖
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,日本日本科学技术振兴机构数据库,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:9981