Displaying similar documents to “Groups with the same orders of Sylow normalizers as the Mathieu groups.”

Finite groups with primitive Sylow normalizers

A. D'Aniello, C. De Vivo, G. Giordano (2002)

Bollettino dell'Unione Matematica Italiana

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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.

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

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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.

Algorithms for permutability in finite groups

Adolfo Ballester-Bolinches, Enric Cosme-Llópez, Ramón Esteban-Romero (2013)

Open Mathematics

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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.