A rather natural way for trying to obtain a lattice-theoretic characterization of a class of groups X is to replace the concepts appearing in the definition of X by lattice-theoretic concepts. The first to use this idea were Kontorovič and Plotkin who in 1954 introduced the notion of modular chain in a lattice, as translation of a central series of a group, to determine a lattice-theoretic characterization of the class of torsion-free nilpotent groups. The aim of this paper is to present a recent application of this translation method to some generalized nilpotency properties.

ON SOME NEW DEVELOPMENTS IN THE THEORY OF SUBGROUP LATTICES OF GROUPS

De Falco M.;Musella C.
2023

Abstract

A rather natural way for trying to obtain a lattice-theoretic characterization of a class of groups X is to replace the concepts appearing in the definition of X by lattice-theoretic concepts. The first to use this idea were Kontorovič and Plotkin who in 1954 introduced the notion of modular chain in a lattice, as translation of a central series of a group, to determine a lattice-theoretic characterization of the class of torsion-free nilpotent groups. The aim of this paper is to present a recent application of this translation method to some generalized nilpotency properties.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/901383
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