| 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. |
| 关键词: 幂自同构 幂零群 内幂零群 极小非SMSN-群 |
| DOI： |
| 分类号:O152.1 |
| 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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| FINITE GROUPS WHOSE ALL MAXIMAL SUBGROUPS ARE SMSN-GROUPS |
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GUO Peng-fei1,2
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1.School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China;2.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. |
| Key words: power automorphisms nilpotent groups minimal non-nilpotent groups minimal non-SMSN-groups |
