SR 2.058

04.12.2025

Marco Amelio (KIT)

15:45 Uhr

Abstract: A group is said to be sharply 2-transitive if it admits an action on a set X such that the induced action on ordered pairs of distinct points of X is regular (as is, for example, the action of the group of one-dimensional affine transformations over a field K, AGL(1,K), on the affine line of K). Until recently, the existence of non-split sharply 2-transitive groups (i.e., sharply 2-transitive groups without a normal abelian subgroup) was an open problem. The first examples of such groups were exhibited by Rips, Segev and Tent in 2017 and by Rips and Tent in 2019. It is possi-ble to associate to every sharply 2-transitive group a characteristic, which is either 0 or a posi-tive prime number. The first of these examples were in characteristic 2, while the others were in characteristic 0, leaving the problem open for odd characteristics. In this talk, I will outline how, in joint work with Simon André and Katrin Tent, we constructed non-split sharply 2-transitive groups for every large enough positive characteristic, and how this can be further modified to obtain bounded exponent non-split sharply 2-transitive groups for large enough characteristic p ≡ 3 (mod 4).

If time permits, I will explain as well how these constructions make use of geometric small can-cellation, and how these methods relate to the 'usual' combinatorial small cancellation.