| 3-极大子群皆正规的有限群 |
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| 引用本文： | 王坤仁.3-极大子群皆正规的有限群[J].四川师范大学学报(自然科学版),2003,26(1):6-9. |
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| 作者姓名： | 王坤仁 |
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| 作者单位： | 四川师范大学,数学与软件科学学院,四川,成都,610066 |
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| 摘 要： | 令n是一个正整数,有限群G的一个子群H被称为G的一个n-极大子群,如果G有一个极大子群链H=Gn＜
*Gn-1＜…＜ *G0=G.此处研究了其n-极极大子群皆在G中正规的有限群G,此处n分别为2和3,并得到了上述两类有限群的分类定理.
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| 关 键 词： | 有限群 3－极大子群 正规子群 幂零群 超可解群 极小非幂零群 分类定理 |
Finite Groups Whose 3-maximal Subgroups are Normal |
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| Abstract.Finite Groups Whose 3-maximal Subgroups are Normal[J].Journal of Sichuan Normal University(Natural Science),2003,26(1):6-9. |
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| Authors: | Abstract |
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| Abstract: | Let n be a positive integer. A subgroup H of a finite group G is called an n-maximal subgorup of G, if there exists a chain of maximal subgroups in G:H=Gn＜ *Gn-1＜…＜ *G0=G. In this paper, the finite groups G whose n-maximal subgroups are normal in G,n=2,3, respectively, are studied and the complete classfication theorems of these two classes of finite groups are obtained. |
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| Keywords: | n-maximal subgroup Normal subgroup Nilpotent group Supersolvable group |
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