### On minimal conditions related to Miller-Moreno type groups

Brunella Bruno, Richard E. Phillips (1983)

Rendiconti del Seminario Matematico della Università di Padova

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Brunella Bruno, Richard E. Phillips (1983)

Rendiconti del Seminario Matematico della Università di Padova

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V. V. Belyaev, M. Kuzucuoğlu, E. Seçkin (1999)

Rendiconti del Seminario Matematico della Università di Padova

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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...

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.

Russo, Francesco (2007)

International Journal of Mathematics and Mathematical Sciences

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Howard Smith, James Wiegold (1994)

Rendiconti del Seminario Matematico della Università di Padova

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Simion Breaz, Grigore Călugăreanu (2002)

Commentationes Mathematicae Universitatis Carolinae

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The notions of nearly-maximal and near Frattini subgroups considered by J.B. Riles in [20] and the natural related notions are characterized for abelian groups.

A. Arikan, T. Özen (2004)

Rendiconti del Seminario Matematico della Università di Padova

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