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几则有限群可解的条件
  • ISSN号：1671-9352
  • 期刊名称：《山东大学学报：理学版》
  • 时间：0
  • 分类：O152.1[理学—数学;理学—基础数学]
  • 作者机构：[1]山西财经大学数学系,山西太原030031
  • 相关基金：国家自然科学基金资助项目（10771132）;山西省高校科技项目（20081022）
作者： 王俊新[1]
关键词： 极大子群, 半覆盖远离性, 极大完备, 可解群, maximal subgroup, semicover-avoiding property, maximal completion, solvable group
中文摘要：

研究了子群的半覆盖远离性质与群的可解性之间的关系，得到了几则有限群可解的充要条件。主要结果为：有限群G可解当且仅当对G的每个极大子群M，或者M是G的半覆盖远离子群，或者肼存在可解的极大完备C，使得C是G的半覆盖远离子群。

英文摘要：

The relationships between the semi cover-avoiding property of subgroups and the solvability of groups are investigated. As an application, some sufficient and necessary conditions for finite groups to be solvable are obtained. It is proved that a finite group G is solvable if and only if for every maximal subgroup M of G, either M is semi cover-avoiding in G, or M has a solvable maximal completion C such that C is semi cover-avoiding in G.

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期刊信息
  • 《山东大学学报：理学版》
  • 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:山东大学
  • 主编：刘建亚
  • 地址：济南市经十路17923号
  • 邮编：250061
  • 邮箱：xblxb@sdu.edu.cn
  • 电话：0531-88396917
  • 国际标准刊号：ISSN：1671-9352
  • 国内统一刊号：ISSN：37-1389/N
  • 邮发代号:24-222
  • 获奖情况:
  • 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）,波兰哥白尼索引,德国数学文摘,中国中国科技核心期刊,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）,英国英国皇家化学学会文摘
  • 被引量:6243