Authors: Jovanović, Jelena
Šešelja, Branimir
Tepavčević, Andreja 
Affiliations: Computer Science 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Lattice characterization of finite nilpotent groups
Journal: Algebra Universalis
Volume: 82
Issue: 3
First page: 40
Issue Date: 1-Aug-2021
Rank: ~M22
ISSN: 0002-5240
DOI: 10.1007/s00012-021-00716-7
The paper deals with subnormal and composition subgroups in the framework of weak congruence lattices of groups. Weak congruences of the composition subgroups of a group form a sublattice of the lattice of all weak congruences. We characterize normality and subnormality in purely lattice-theoretic terms. For a finite group G we prove: all subgroups of G are subnormal (i.e., G is nilpotent) if and only if the weak congruence lattice of G is lower semimodular.
Keywords: Finite nilpotent groups | Semi-modularity | Subnormal subgroups | Weak congruence lattice
Publisher: Springer Link

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