| 所有极大子群都为SMSN-群的有限群 |
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| 引用本文： | 郭鹏飞.所有极大子群都为SMSN-群的有限群[J].数学杂志,2017,37(4):714-722. |
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| 作者姓名： | 郭鹏飞 |
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| 作者单位： | 海南师范大学数学与统计学院, 海南 海口 571158;连云港师范高等专科学校数学与信息工程学院, 江苏 连云港 222006 |
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| 基金项目： | Supported by National Natural Science Foundation of China (11661031); Jiangsu Overseas Research & Training Program for University Prominent Young & Middle-Aged Teachers and Presidents; "333" Project of Jiangsu Province(BRA2015137); "521" Project of Lianyungang City. |
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| 摘 要： | 若有限群G的每个2-极大子群在G中次正规,则称G为SMSN-群.本文研究了有限群G的每个真子群是SMSN-群但G本身不是SMSN-群的结构,利用局部分析的方法,获得了这类群的完整分类,推广了有限群结构理论的一些成果.
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| 关 键 词： | 幂自同构 幂零群 内幂零群 极小非SMSN-群 |
| 收稿时间： | 2015/9/6 0:00:00 |
| 修稿时间： | 2015/12/3 0:00:00 |
FINITE GROUPS WHOSE ALL MAXIMAL SUBGROUPS ARE SMSN-GROUPS |
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| GUO Peng-fei.FINITE GROUPS WHOSE ALL MAXIMAL SUBGROUPS ARE SMSN-GROUPS[J].Journal of Mathematics,2017,37(4):714-722. |
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| Authors: | GUO Peng-fei |
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| Institution: | School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China;School of Mathematics and Information Engneering, Lianyungang Normal College, Lianyungang 222006, China |
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| Abstract: | A flnite group G is called an SMSN-group if its 2-maximal subgroups are subnormal in G. In this paper, the author investigates the structure of flnite groups which are not SMSN-groups but all their proper subgroups are SMSN-groups. Using the idea of local analysis, a complete classiflcation of this kind of groups is given, which generalizes some results of the structure of flnite groups. |
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| Keywords: | power automorphisms nilpotent groups minimal non-nilpotent groups minimal non-SMSN-groups |
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