Felix-Klein-Kolloquium des Fachbereichs

One natural way to explore the structure of an infinite discrete group is to study its proper quotient groups. This problem often splits into two subproblems that happen to require fundamentally different methods: the study of finite quotients versus that of infinite quotients. It turns out that this dichotomy has played an important role in the construction of several families of infinite simple groups of various kind. The goal of this talk is to illustrate this paradigm by means of explicit examples, including multiplicative groups of division algebras over number fields, and Gromov hyperbolic groups.