| 合成群列数较少的有限可解群 |
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| 引用本文： | 朱一心,刘燕俊,海进科,范兴亚. 合成群列数较少的有限可解群[J]. 首都师范大学学报(自然科学版), 2010, 31(6) |
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| 作者姓名： | 朱一心 刘燕俊 海进科 范兴亚 |
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| 作者单位： | 首都师范大学数学科学学院;北京大学数学科学学院;青岛大学数学系; |
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| 摘 要： | 对于有限群G,记CS(G)和PS(G)分别为G的所有合成群列和主群列的集合,这两个集合中的元素个数∣CS(G) ∣和∣PS(G) ∣在一定程度上决定了G的结构.本文分别给出了∣CS(G) ∣=2,3时可解群G的结构和∣PS(G)∣=2,3时超可解群G的结构.
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| 关 键 词： | 有限可解群 有限超可解群 合成群列 主群列 |
Finite Groups With Small Number of Composition Series |
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| Zhu Yixin,Liu Yanjun,Hai Jinke,Fan Xingya. Finite Groups With Small Number of Composition Series[J]. Journal of Capital Normal University(Natural Science Edition), 2010, 31(6) |
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| Authors: | Zhu Yixin Liu Yanjun Hai Jinke Fan Xingya |
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| Affiliation: | Zhu Yixin1 Liu Yanjun2 Hai Jinke3 Fan Xingya1(1.School of Mathematical Science,Capital Normal University,Beijing 100048,2.School of Mathematical Science,Beijing University,Beijing 100871,3.Department of Mathematics,Qingdao University,Qingdao 266071) |
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| Abstract: | Let G be a finite group and let CS(G) and PS(G) be the sets of all composition series and principal series of G respectively.The number | CS(G) |(respectively,| PS(G) |) of elements of the set CS(G)(respectively,PS(G)) to some extent determines the structure of G.In this paper,we investigate the cases that |CS(G) | = 2,3 and | PS(G) | = 2,3 under the assumption that G is solvable and supersolvable respectively.Our main purpose is to get the characterizations of such groups. |
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| Keywords: | finite soluble group finite supersoluble groups composition seriers principal seriers. |
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