Speaker: Sofia Brenner (Kassel)
Title: Irredundant Base Sizes of Solvable Permutation Groups (and some Connections to Model Theory)
Abstract:
An irredundant base of a permutation group \(G\) on a finite set \(\Omega\) is a sequence of points \((\omega_1, \dots, \omega_k)\) in \(\Omega\) such that the chain of pointwise stabilizers \(G > G_{\omega_1} > G_{\omega_1, \omega_2} > \dots > G_{\omega_1, \dots, \omega_k} = 1\) refines with each new point and only the identity fixes all points in the sequence. We determine asymptotically tight bounds for the maximal size of an irredundant base for solvable permutation groups. If time permits, I will explain some connections to extendability properties of partial automorphisms, a concept from model theory. This is based on joint work with Coen del Valle and Colva Roney-Dougal.