| OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U6（2） |
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| 引用本文： | 张良才,施武杰.OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U6（2）[J].数学物理学报(B辑英文版),2011,31(2):441-450. |
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| 作者姓名： | 张良才 施武杰 |
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| 作者单位： | College of Mathematics and Statistics;Chongqing University;School of Mathematics and Statistics;Chongqing University of Arts and Sciences; |
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| 基金项目： | supported by Natural Science Foundation Project of CQ CSTC (2010BB9206); NNSF of China (10871032); Fundamental Research Funds for the Central Universities (Chongqing University, CDJZR10100009); National Science Foundation for Distinguished Young Scholars of China (11001226) |
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| 摘 要： | Let G be a finite group and π(G) = { p 1 , p 2 , ··· , p k } be the set of the primes dividing the order of G. We define its prime graph Γ(G) as follows. The vertex set of this graph is π(G), and two distinct vertices p, q are joined by an edge if and only if pq ∈π e (G). In this case, we write p ～ q. For p ∈π(G), put deg(p) := |{ q ∈π(G) | p ～ q }| , which is called the degree of p. We also define D(G) := (deg(p 1 ), deg(p 2 ), ··· , deg(p k )), where p 1 < p 2 < ··· < p k , which is called the degree pattern of G. We say a group G is k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups with the same order and degree pattern as G. Specially, a 1-fold OD-characterizable group is simply called an OD-characterizable group. Let L := U 6 (2). In this article, we classify all finite groups with the same order and degree pattern as an almost simple groups related to L. In fact, we prove that L and L.2 are OD-characterizable, L.3 is 3-fold OD-characterizable, and L.S 3 is 5-fold OD-characterizable.
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| 关 键 词： | 外径 表征 单群 有限群 顶点集 二甘醇 定义 素数 |
OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U_6(2) |
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| Zhang Liangcai College of Mathematics , Statistics,Chongqing University,Shapingba ,China Shi Wujie School of Mathematics , Statistics,Chongqing University of Arts , Sciences,Youngchuan ,China.OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U_6(2)[J].Acta Mathematica Scientia,2011,31(2):441-450. |
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| Authors: | Zhang Liangcai College of Mathematics Statistics Chongqing University Shapingba China Shi Wujie School of Mathematics Statistics Chongqing University of Arts Sciences Youngchuan China |
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| Institution: | Zhang Liangcai College of Mathematics and Statistics,Chongqing University,Shapingba 401331,China Shi Wujie School of Mathematics and Statistics,Chongqing University of Arts and Sciences,Youngchuan 402160,China |
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| Abstract: | Let G be a finite group and π(G) = { p 1 , p 2 , · · · , p k } be the set of the primes dividing the order of G. We define its prime graph Γ(G) as follows. The vertex set of this graph is π(G), and two distinct vertices p, q are joined by an edge if and only if pq ∈ π e (G). In this case, we write p ～ q. For p ∈ π(G), put deg(p) := |{ q ∈ π(G) | p ～ q }| , which is called the degree of p. We also define D(G) := (deg(p 1 ), deg(p 2 ), · · · , deg(p k )), where p 1 < p 2 < · · · < p k , which is called the degree pattern of G. We say a group G is k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups with the same order and degree pattern as G. Specially, a 1-fold OD-characterizable group is simply called an OD-characterizable group. Let L := U 6 (2). In this article, we classify all finite groups with the same order and degree pattern as an almost simple groups related to L. In fact, we prove that L and L.2 are OD-characterizable, L.3 is 3-fold OD-characterizable, and L.S 3 is 5-fold OD-characterizable. |
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| Keywords: | Almost simple group prime graph degree of a vertex degree pattern |
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