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.
@article{urn:eudml:doc:42396,
title = {Classification of finite groups with many minimal subgroups and with the number of conjugacy classes of G/S(G) equal to 8.},
journal = {Collectanea Mathematica},
volume = {41},
year = {1990},
pages = {243-279},
zbl = {0824.20027},
mrnumber = {MR1163905},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42396}
}
Vera López, Antonio; Arregi Lizarraga, Jesús María; Vera López, Francisco José. Classification of finite groups with many minimal subgroups and with the number of conjugacy classes of G/S(G) equal to 8.. Collectanea Mathematica, Tome 41 (1990) pp. 243-279. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42396/