On the representation of lattices by subgroup lattices
by
Vladimir Repnitskii
Ural State University, Ekaterinburg, Russia

For a group G, we denote by Sub G the lattice of subgroups of G. Given a class K of groups, we call a lattice L representable by the subgroup lattice of a group from K if L is embeddable in Sub G for some group G in K. Lat K denotes the class of all lattices which are representable by subgroup lattices of groups from K. In our lecture we discuss some questions concerning connections between K and Lat K for natural classes K of groups. In addition, we discuss a new proof of J.T\.uma's result (1986) about that every algebraic lattice is isomorphic to an interval in the subgroup lattice of a suitable (infinite) group.

Date received: May 17, 2004