**Speaker:** Rebecca Waldecker (Halle)

**Title:** *Permutation Groups Where Non-Trivial Elements Have Few Fixed Points*

**Abstract:**
Motivated by the theory of Riemann surfaces, we look at finite
permutation groups where non-trivial elements have few, that is at
most four, fixed points. We do not look at regular actions or
Frobenius groups, but instead begin with the case with at most two
fixed points.

There are classical results if additional restrictions are imposed, for example 2-transitivity, but without such a hypothesis there is quite some work to do. We prove a general result and classify all simple examples. In the next case we also allow three fixed points, and I'll talk about the current state of our work.

This is a joint project with Kay Magaard (Birmingham), supported by the DFG.