Hyperbolic groups acting sharply 2- or 3-transitively and the Burnside problem (C04)

• Subject Area: Mathematics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 427320536

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.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1442: Geometry: Deformations and Rigidity
• Applicant Institution: Universität Münster
• Project Head: Professorin Dr. Katrin Tent