Classification of finite groups according to the number of conjugacy classes II |
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Authors: | Antonio Vera López Juan Vera López |
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Institution: | (1) Departamento de Matemáticas, Facultad de Ciencias, Universidad del Pais Vasco, Apartado 644, Bilbao, Spain;(2) Instituto Nacional de Bachillerato, Cura Valera, Huercal-Overa, Almeria, Spain |
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Abstract: | 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) =n −a 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. |
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Keywords: | |
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