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

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It is a consequence of the classification of finite simple groups that every non-abelian simple group contains a subgroup which is a minimal simple group.

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In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.

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Finite groups with primitive Sylow normalizers

A. D&amp;#039;Aniello, C. De Vivo, G. Giordano (2002)

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We prove that are primitive the finite groups whose normalizers of the Sylow subgroups are primitive. We classify the groups of such class, denoted by $N P$ , and we study the Schunck classes whose boundary is contained in $N P$ . We give also necessary and sufficient conditions in order that the projectors be subnormally embedded.