22-11-2019 at 2pm
TITLE: Abelian and nilpotent covers of finite groups
ABSTRACT: A COVER of a finite group G is a set of subgroups of the group G whose union is the full group. In this group we are interested in covers where the subgroups in question are of a certain prescribed type (e.g. abelian or nilpotent). Our interest is in finding the size of the smallest such covers. In the talk we will study this question for the case when G is dihedral, and we will give some hints about what happens with more complicated groups like the symmetric group.