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

Antonio Vera López; Jesús María Arregi Lizarraga; Francisco José Vera López — 1990

Collectanea Mathematica

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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