%0 Journal Article
%T On some new developments in the theory of subgroup lattices of groups
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A De Falco, Maria
%A Musella, Carmela
%D 2023
%\ 09/01/2023
%V 12
%N 3
%P 153-162
%! On some new developments in the theory of subgroup lattices of groups
%K modular lattice
%K permodular subgroup
%K permodular chain
%R 10.22108/ijgt.2022.132076.1771
%X A rather natural way for trying to obtain a lattice-theoretic characterization of a class of groups ${\mathcal X}$ is to replace the concepts appearing in the definition of ${\mathcal X}$ by lattice-theoretic concepts. The first to use this idea were Kontorovi\v{c} 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.
%U https://ijgt.ui.ac.ir/article_26618_4fa5889b4b31542b0c65fb633b016ce6.pdf