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内PN^＊-群的结构
  • ISSN号：1000-0917
  • 期刊名称：《数学进展》
  • 时间：0
  • 分类：O152.1[理学—数学;理学—基础数学]
  • 作者机构：[1]连云港师范高等专科学校数学系,连云港江苏222006, [2]上海大学上海市应用数学和力学研究所,上海200072, [3]上海大学数学系,上海200444, [4]宁波工程学院理学院,宁波浙江315211
  • 相关基金：Acknowledgements The authors are indebted to the referees for their valuable suggestions and comments which polish this paper largely.Foundation item： Supported by NSFC（No. 10771132） and Qing Lan Project of Jiangsu Province.
作者： 郭鹏飞[1,2], 葛仁福[2], 张小红[3,4]
关键词： 正规子群, PN^＊-群, 内PN^＊-群, 超可解群, normal subgroup, PN＊-group, minimal non-PN＊-group, supersolvable group
中文摘要：

若有限群G的每个极小子群及4阶循环子群在G中正规，则称G为PN^＊-群．本文给出了有限群的每个真子群都是PN^＊-群但其本身不是PN^＊-群的完全分类．

英文摘要：

A finite group G is called a PN＊-group if all minimal subgroups and all cyclic subgroups with order 4 of G are normal in G. In this paper, we give a complete classification of those finite groups which are not PN＊-groups but whose proper subgroups are all PN＊-groups.

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期刊信息
  • 《数学进展》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学协术学会
  • 主办单位:中国数学会
  • 主编：丁伟岳
  • 地址：北京大学数学系数学进展编辑部
  • 邮编：100871
  • 邮箱：
  • 电话：
  • 国际标准刊号：ISSN：1000-0917
  • 国内统一刊号：ISSN：11-2312/O1
  • 邮发代号:2-503
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,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:3411