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On the Cantor-Bendixson rank of metabelian groups

Yves Cornulier (2011)

Annales de l’institut Fourier

We study the Cantor-Bendixson rank of metabelian and virtually metabelian groups in the space of marked groups, and in particular, we exhibit a sequence ( G n ) of 2-generated, finitely presented, virtually metabelian groups of Cantor-Bendixson rank  ω n .

On the lattice of pronormal subgroups of dicyclic, alternating and symmetric groups

Shrawani Mitkari, Vilas Kharat (2024)

Mathematica Bohemica

In this paper, the structures of collection of pronormal subgroups of dicyclic, symmetric and alternating groups G are studied in respect of formation of lattices L ( G ) and sublattices of L ( G ) . It is proved that the collections of all pronormal subgroups of A n and S n do not form sublattices of respective L ( A n ) and L ( S n ) , whereas the collection of all pronormal subgroups LPrN ( Dic n ) of a dicyclic group is a sublattice of L ( Dic n ) . Furthermore, it is shown that L ( Dic n ) and LPrN ( Dic n ) are lower semimodular lattices.

On the structure of groups whose non-abelian subgroups are subnormal

Leonid Kurdachenko, Sevgi Atlıhan, Nikolaj Semko (2014)

Open Mathematics

The main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.

On transitivity of pronormality

Leonid A. Kurdachenko, Igor Ya. Subbotin (2002)

Commentationes Mathematicae Universitatis Carolinae

This article is dedicated to soluble groups, in which pronormality is a transitive relation. Complete description of such groups is obtained.

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