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.. - In: INTERNATIONAL JOURNAL OF GROUP THEORY. - ISSN 2251-7650. - 12:3(2023), pp. 153-162. [10.22108/ijgt.2022.132076.1771]
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
