| 内SMSN-群的结构 |
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| 引用本文： | 郭鹏飞,赵先鹤.内SMSN-群的结构[J].河南师范大学学报(自然科学版),2012,40(1):24-26. |
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| 作者姓名： | 郭鹏飞 赵先鹤 |
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| 作者单位： | 1. 连云港师范高等专科学校数学系,江苏连云港222006;上海大学上海市应用数学与力学研究所,上海200072
2. 河南师范大学数学与信息科学学院,河南新乡,453007 |
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| 基金项目： | 国家自然科学基金，山西省国土资源厅项目 |
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| 摘 要： | 有限群G的子群H称为G的半正规子群,若H与G的每个满足条件(|K|,|H|)=1的子群K使得HK=KH成立.若有限群G的每个Sylow子群的极大子群都在G中半正规,则称G为SMSN-群.给出内SMSN-群(群G的每个真子群是SMSN-群但G本身不是SMSN-群)的分类.
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| 关 键 词： | 半正规子群 超可解群 内幂零群 内超可解群 |
The Structure of Minimal Non-SMSN-Groups |
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| GUO Peng-fei
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ZHAO Xian-he.The Structure of Minimal Non-SMSN-Groups[J].Journal of Henan Normal University(Natural Science),2012,40(1):24-26. |
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| Authors: | GUO Peng-fei ZHAO Xian-he |
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| Institution: | 1.Department of Mathematics,Lianyungang Teacher’s College,Lianyungang 222006,China;2.Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,China;3.College of Mathematics & Information Science,Henan Normal University,Xinxiang 453007,China) |
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| Abstract: | A subgroup H of a finite group G is called a seminormal subgroup of G if HK=KH for every subgroup K with(|K|,|H|)=1.A finite group G is called an SMSN-group if all maximal subgroups of the Sylow subgroups of G are seminormal in G.This paper has given a classification of minimal non-SMSN-groups(groups which are not SMSN-groups but whose proper subgroups are all SMSN-groups). |
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| Keywords: | seminormal subgroups supersolvable groups minimal non-nilpotent groups minimal non-supersolvable groups |
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