Czechoslovak Mathematical Journal

, Volume 60, Issue 4, pp 945–950 | Cite as

Intersection graphs of subgroups of finite groups

  • Rulin Shen


In this paper we classify finite groups with disconnected intersection graphs of subgroups. This solves a problem posed by Csákány and Pollák.


intersection graphs finite groups subgroups 

MSC 2010

20D60 20D06 


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  1. [1]
    M. Aschbacher: On the maximal subgroups of the finite classical groups. Invent. Math. 76 (1984), 469–514.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    J. Bosák: The graphs of semigroups. Theory Graphs Appl., Proc. Symp. Smolenice 1963. 1964, pp. 119–125.Google Scholar
  3. [3]
    R. Carter: Simple Groups of Lie Type. Wiley, London, 1972.MATHGoogle Scholar
  4. [4]
    I. Chakrabarty, S. Ghosh, T.K. Mukherjee, M.K. Sen: Intersection graphs of ideals of rings. Electronic Notes in Discrete Mathematics 23 (2005), 23–32.CrossRefMathSciNetGoogle Scholar
  5. [5]
    B. Csákéany, G. Pollák: The graph of subgroups of a finite group. Czechoslovak Math. J. 19 (1969), 241–247.MathSciNetGoogle Scholar
  6. [6]
    A. S. Kondrat’ev: Prime graph components of finite simple groups. Math. USSR Sb. 67 (1989), 235–247.CrossRefGoogle Scholar
  7. [7]
    D. J. S. Robinson: A Course in the Theory of Groups. Springer, New York-Heidelberg- Berlin, 1982.MATHGoogle Scholar
  8. [8]
    J. S. Williams: Prime graph components of finite groups. J. Algebra 69 (1981), 487–513.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    B. Zelinka: Intersection graphs of finite abelian groups. Czech. Math. J. 25 (1975), 171–174.MathSciNetGoogle Scholar

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2010

Authors and Affiliations

  1. 1.EnshiP.R.China
  2. 2.Department of MathematicsHubei University for NationalitiesEnshi, HubeiP.R.China

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