Israel Journal of Mathematics

, Volume 56, Issue 2, pp 188–221 | Cite as

Classification of finite groups according to the number of conjugacy classes II

  • Antonio Vera López
  • Juan Vera López


In the following,G denotes a finite group,r(G) the number of conjugacy classes ofG, β(G) the number of minimal normal subgroups ofG andα(G) the number of conjugate classes ofG not contained in the socleS(G). Let Φ j = {G|β(G) =r(G) −j}. In this paper, the family Φ11 is classified. In addition, from a simple inspection of the groups withr(G) =b conjugate classes that appear in ϒ j =1/11 Φ j , we obtain all finite groups satisfying one of the following conditions: (1)r(G) = 12; (2)r(G) = 13 andβ(G) > 1; …; (9)r(G) = 20 andβ(G) > 8; (10)r(G) =n andβ(G) =na with 1 ≦a ≦ 11, for each integern ≧ 21. Also, we obtain all finite groupsG with 13 ≦r(G) ≦ 20,β(G) ≦r(G) − 12, and satisfying one of the following conditions: (i) 0 ≦α(G) ≦ 4; (ii) 5 ≦α(G) ≦ 10 andS(G) solvable.


Finite Group Conjugacy Class Simple Group Minimal Normal Subgroup Frobenius Group 
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Copyright information

© Hebrew University 1986

Authors and Affiliations

  • Antonio Vera López
    • 1
  • Juan Vera López
    • 2
  1. 1.Departamento de Matemáticas, Facultad de CienciasUniversidad del Pais VascoBilbaoSpain
  2. 2.Instituto Nacional de Bachillerato, Cura ValeraHuercal-Overa, AlmeriaSpain

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