# Darstellungstheorietage and Nikolaus Conference 2013

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.