Displaying similar documents to “On minimal length factorizations of finite groups.”

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.

On small distances of small 2-groups

Natalia Zhukavets (2001)

Commentationes Mathematicae Universitatis Carolinae

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The paper reports the results of a search for pairs of groups of order n that can be placed in the distance n 2 / 4 for the case when n ∈ { 16 , 32 } . The constructions that are used are of the general character and some of their properties are discussed as well.

Simple group contain minimal simple groups.

Michael J. J. Barry, Michael B. Ward (1997)

Publicacions Matemàtiques

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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.