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特殊射影线性群L_5(q)的OD-刻画 被引量：1

OD-Characterization of Some Projective Special Linear Group L_5(q)
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摘要 若存在k个互不同构的群与群G具有相同的群阶和素图度数序列,则称群G是可k重OD-刻画的.特别地,若k=1,则称群G是OD-刻画群.利用群阶和素图度数序列证明了特殊射影线性群L5(q)是OD-刻画群,其中q(2≤q<15)是素数的方幂. A group Gis called k-fold OD-characterizable if there exist exactly k non-isomorphic groups M with the same order and degree pattrn as M.In particular,a 1-fold OD-characterizable group is simply called an OD-characterizable group.In this paper,it has beenproved that projective special linear group L5（q）is OD-characterizable by the order and degree pattern,where q（2≤q〈15）is the power of prime.
作者 张盟盟 张良才 包奕
机构地区 重庆人文科技学院机电与信息工程学院 重庆大学数学与统计学院
出处 《西南师范大学学报（自然科学版）》 CAS 北大核心 2016年第6期1-5,共5页 Journal of Southwest China Normal University(Natural Science Edition)
基金 国家自然科学基金项目(11401324 11271301 11471266) 国家青年科学基金项目(11401324) 教育部第47批留学回国人员科研启动基金项目 重庆市自然科学基金项目(cstc2014jcyjA0148)
关键词 有限单群 顶点度数 特殊射影线性群 finite simple group degree pattern projective special linear group
分类号 O152.3 [理学—基础数学]
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参考文献8

  • 1WILLIAMS J S. Prime Graph Components of Finite Group [J]. Journal of Algebra, 1981, 69(2) : 487--513.
  • 2CONWAY J H, CURTIS R T, NORTON S P, et al. Atlas of Finite Groups [M]. London: Clarendon Press Oxford, 1985.
  • 3ZHANG L C, SHI W J. OD-Characterization of All Simple Groups Whose Orders are Less Than 108 [J]. Front Math China, 2008, 3(3): 461--474.
  • 4ZAVARNITSINE A V. Finite Simple Groups with Narrow Prime Spectrum [J]. Siberian Elektronic Mathematical Re- ports, 2008(2): 1--12.
  • 5VASIL'EV A V, VDOVIN E P. An Adjacency Criterion for the Prime Graph of a Finite Simple Group [J]. Algebra and Logic, 2005, 44(6): 682--725.
  • 6MOGHADDAMFAR A R, ZOKAYI A R, DARAFSHEH M R. A Characterization of Finite Simple Groups by the De- grees of Vertices of Their Prime Graphs [J]. Algebra Colloquium, 2005, 12(3): 431--442.
  • 7IRANMANESH A, ALAVI S H. A Characterisation of Simple Groups PSL(5, q) [J]. Bull Austral Math Soc, 2002, 65(2) : 211--222.
  • 8张良才,吕恒,余大鹏,陈顺民.有限单群L_6(5)的OD-刻画(英文)[J].西南大学学报（自然科学版）,2011,33(12):82-85. 被引量：4

二级参考文献8

  • 1WILLIAMS J S. Prime Graph Components of Finite Groups [J]. Journal of Algebra, 1981, 69(2) : 487-513.
  • 2CONWAY J H, CURTIS R T, NORTON S P, et al. Atlas of Finite Groups [M]. London: Clarendon Press (Oxford), 1985.
  • 3MOGHADDAMFAR A R, ZOKAYI A R, DARAFSHEH M R. A Characterization of Finite Simple Groups by the De- grees of Vertices of Their Prime Graphs [J]. Algebra Colloquium, 2005, 12(3): 431-442.
  • 4ZHANG Liang-cai, LIU Xue-feng. Characterization of the Projective General Linear Groups PGL(2, q) by Their Orders and Degree Patterns [J]. International Journal of Algebra and Computation, 2009, 19 (7) .. 873 - 889.
  • 5DARAFSHEH M R. Order of Elements in the Groups Related to the General Linear Group EJ~. Finite Field and Their Applications, 2005, 11.. 738-747.
  • 6VASIL'EV A V, VDOVIN E P. An Adjacency Criterion for the Prime Graph of a Finite Simple Group I-J]. Algebra and Logic, 2005, 44(6): 381-406.
  • 7VASIL'EV A V. On Connection Between the Structure of a Finite Group and the Properties of Its Prime Graph [J]. Si- berian Mathematical Journal, 2005, 46(3): 396-404.
  • 8ZAVARNITSINE A V. Finite Simple Groups with Narrow Prime Spectrum [J]. Siberian Electronic Mathematical Re- ports, 2009(6): 112.

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西南师范大学学报（自然科学版）
2016年 第6期

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