Authors: Grulović, Milan
Jovanović, Jelena
Šešelja, Branislav
Tepavčević, Andreja 
Affiliations: Computer Science 
Title: Lattice characterization of some classes of groups by series of subgroups
Journal: International Journal of Algebra and Computation
Issue Date: 2022
Rank: ~M23
ISSN: 0218-1967
DOI: 10.1142/S0218196723500121
In this paper, we characterize several classes of groups by the properties of their weak congruence lattices. Namely, we give necessary and sufficient conditions for the weak congruence lattice of a group, under which this group is a T-group, T-group, metacyclic, cocyclic, hyperabelian, polycyclic, N-group and Ñ-group. We also discuss groups for which all subgroups are simple, like the Tarski monsters, and we show that they represent a class of non-Dedekind groups with a particular embedding property for lattices of normal subgroups. All the mentioned characterized groups are related to (different) series of subgroups, and we represent these series as chains of intervals in the weak congruence lattice. The corresponding conditions are formulated in a purely lattice-Theoretic language.
Publisher: World Scientific

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