OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U6(2)

doi:10.1016/S0252-9602(11)60244-0

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (2): 441-450.doi: 10.1016/S0252-9602(11)60244-0

OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U₆(2)

张良才¹, 施武杰²

1.College of Mathematics and Statistics, Chongqing University, Shapingba 401331, China|2.School of Mathematics and Statistics, Chongqing University of Arts and Sciences, Youngchuan 402160, China

收稿日期:2007-11-06 修回日期:2010-10-27 出版日期:2011-03-20 发布日期:2011-03-20
基金资助:
This work is partly supported by Natural Science Foundation Project of CQ CSTC (2010BB9206), NNSF of China (10871032), Fundamental Research Funds for the Central Universities (Chongqing University, CDJZR10100009), and National Science Foundation for Distinguished Young Scholars of China (11001226)

OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U₆(2)

ZHANG Liang-Cai¹, SHI Wu-Jie²

1.College of Mathematics and Statistics, Chongqing University, Shapingba 401331, China|2.School of Mathematics and Statistics, Chongqing University of Arts and Sciences, Youngchuan 402160, China

Received:2007-11-06 Revised:2010-10-27 Online:2011-03-20 Published:2011-03-20
Supported by:
This work is partly supported by Natural Science Foundation Project of CQ CSTC (2010BB9206), NNSF of China (10871032), Fundamental Research Funds for the Central Universities (Chongqing University, CDJZR10100009), and National Science Foundation for Distinguished Young Scholars of China (11001226)

摘要/Abstract

摘要：

Let G be a finite group and π(G)={p₁, p₂, …, 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(p₁), deg(p₂), … , deg(p_k)), where p₁<p₂<…<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:=U₆(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.S₃ is 5-fold OD-characterizable.

关键词: Almost simple group, prime graph, degree of a vertex, degree pattern

Abstract:

Key words: Almost simple group, prime graph, degree of a vertex, degree pattern

中图分类号:

20D05

张良才, 施武杰. OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U₆(2)[J]. 数学物理学报(英文版), 2011, 31(2): 441-450.

ZHANG Liang-Cai, SHI Wu-Jie. OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U₆(2)[J]. Acta mathematica scientia,Series B, 2011, 31(2): 441-450.

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OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U₆(2)

OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U₆(2)

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