Authors: Jovanović, Jelena
Šešelja, Branimir
Tepavčević, Andreja 
Affiliations: Computer Science 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Lattices with normal elements
Journal: Algebra Universalis
Volume: 83
First page: 2
Issue Date: 29-Nov-2021
Rank: ~M22
ISSN: 0002-5240
DOI: 10.1007/s00012-021-00759-w
By several postulates we introduce a new class of algebraic lattices, in which a main role is played by so called normal elements. A model of these lattices are weak-congruence lattices of groups, so that normal elements correspond to normal subgroups of subgroups. We prove that in this framework many basic structural properties of groups turn out to be lattice-theoretic. Consequently, we give necessary and sufficient conditions under which a group is Hamiltonian, Dedekind, abelian, solvable, supersolvable, metabelian, finite nilpotent. These conditions are given as lattice-theoretic properties of a lattice with normal elements.
Keywords: Classes of groups | Lattice of subgroups | Lattice of weak congruences | Special elements in lattices
Publisher: Springer Link

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