Branimir Seselja – Lattice characterization of some classes of groups

University of Novi Sad, Serbia, retired professor

By several postulates we introduce a new class of algebraic lattices, in which a main role play 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.
Joint research with A.Tepavcevic and J.Jovanovic