CRC 1442: Geometry: Deformation and Rigidity - C04: Hyperbolic groups acting sharply 2- or 3-transitively and the Burnside problem

Basic data for this project

Type of project: Subproject in DFG-joint project hosted at University of Münster
Duration: 01/07/2020 - 30/06/2024 | 1st Funding period

Description

Until recent 'free' constructions of the PI and her collaborators, the only known sharply 2- and 3-transitive permutation groups were those arising from linear transformations of the affine or projective line. We will investigate the limitations of this class of groups. The quest for sharply 2- and 3-transitive groups in positive characteristic not arising from linear transformations leads us to the Burnside problem, for which we propose a new approach yielding much lower bounds on the exponent for infinite such groups.

Keywords: Geometry; Topology; Group Theory; Mathematics