Displaying similar documents to “Groups with minimal conditions related to finiteness properties on conjugacy classes”

On totally inert simple groups

Martyn Dixon, Martin Evans, Antonio Tortora (2010)

Open Mathematics

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A subgroup H of a group G is inert if |H: H ∩ H g| is finite for all g ∈ G and a group G is totally inert if every subgroup H of G is inert. We investigate the structure of minimal normal subgroups of totally inert groups and show that infinite locally graded simple groups cannot be totally inert.

Groups with Restricted Conjugacy Classes

de Giovanni, F., Russo, A., Vincenzi, G. (2002)

Serdica Mathematical Journal

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Let F C 0 be the class of all finite groups, and for each nonnegative integer n define by induction the group class FC^(n+1) consisting of all groups G such that for every element x the factor group G/CG ( <x>^G ) has the property FC^n . Thus FC^1 -groups are precisely groups with finite conjugacy classes, and the class FC^n obviously contains all finite groups and all nilpotent groups with class at most n. In this paper the known theory of FC-groups is taken as a model, and it...

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.