on some new developments in the theory of subgroup lattices of groups

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 kontoroviˇc 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.