Annali di Matematica Pura ed Applicata

, Volume 150, Issue 1, pp 299–309 | Cite as

About the finite groups whose minimal normal subgroups are union of two conjugacy classes exactly

  • Antonio Vera López
  • Juan Vera López


In this paper we classify all the finite groups G satisfying β(G)=r(G) — α(G) - 1 where r(G) is the number of conjugacy classes of G, β(G) the number of minimal normal subgroups of G, S(G) the socle of G and α(G) the number of conjugacy classes of G out of S(G), and such that ¦G/S(G)¦ is divisible for at most three prime numbers.


Normal Subgroup Finite Group Prime Number Conjugacy Class Minimal Normal Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    W.Burnside,Theory of Groups of Finite Order, 2nd ed. Dover, 1955.Google Scholar
  2. [2]
    D. Gorenstein,Finite Groups, Harper and Row, New York, 1968.Google Scholar
  3. [3]
    M. Hall - J. Senior,The groups of order 2n, n⩽6, MacMillan, New York, 1964.Google Scholar
  4. [4]
    B.Huppert,Endliche Gruppen I, Berlin-Heidelberg, New York, 1967.Google Scholar
  5. [5]
    E. Rodemich,The groups of order 128, J. Algebra,67 (1980), pp. 129–142.Google Scholar
  6. [6]
    A.Vera-López,Dos propiedades relativas al problema de la clasifieaeión de los grupos finitos por el numero de clases de conjugación y el de normales minimales, to appear in Rev. Acad. Ciencias de Madrid.Google Scholar
  7. [7]
    A. Vera-López,Clasificación de grupos finitos con muchos normales minimales y con numero de clases de conjugación de G/S(G) menor que 7, Rev. Acad. Ciencias de Zaragoza,38 (1983), pp. 21–30.Google Scholar
  8. [8]
    A. Vera-López -J. Vera-López,Classification of finite groups according to the number of conjugacy classes, Israel J. Math.,51 (1985), pp. 305–338.Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1987

Authors and Affiliations

  • Antonio Vera López
    • 1
  • Juan Vera López
    • 2
  1. 1.Facultad de Ciencias, Departamento de MatemáticasUniversidad del País VascoBilbaoSpain
  2. 2.Instituto Nacional de Bachillerato Cura Valera HuercalOvera AlmeriaSpain

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