Leírás
The lattice-theoretic characterization of the class of solvable groups was highlighted by R. Schmidt in his 2011 book „Subgroup lattices of groups“ as one of the ”most exciting open problems” in this context. In a series of papers published last 1-2 years, we gave lattice-theoretical characterization not only of solvable groups but many other classes of groups, like nilpotent, abelian, supersolvable, metabelian, and others. One of the first results in this direction was a characterization of Dedekind groups by modular lattices of weak congruences (together with G.Czédli and M.Erne). In this presentation, besides the new results in this direction, we will also tackle the problem of the representation of algebraic lattice by a weak congruence lattice of a group. The results are joint work with Milan Grulovic, Jelena Jovanovic, and Branimir Seselja.