Classification of finite groups with many minimal subgroups and with the number of conjugacy classes of G/S(G) equal to 8

  1. Vera López, Antonio
  2. Arregi Lizarraga, Jesús María
  3. Vera López, Francisco José
Journal:
Collectanea mathematica

ISSN: 0010-0757

Year of publication: 1990

Volume: 41

Fascicle: 3

Pages: 243-279

Type: Article

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Abstract

In this paper we classify all the finite groups satisfying r(G/S(G))=8 and ß(G)=r(G) - a(G) - 1, where r(G) is the number of conjugacy classes of G, ß(G) is the number of minimal normal subgroups of G, S(G) the socle of G and a(G) the number of conjugacy classes of G out of S(G). These results are a contribution to the general problem of the classification of the finite groups according to the number of conjugacy classes.

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