Speaker: Sofia Brenner (Darmstadt)
Title: Tuple Regularity and \(k\)-Ultrahomogeneity for Finite Groups
Abstract:
Studying finite groups from a combinatorial perspective leads to a demand for combinatorial symmetry and regularity measures. In this context, we develop the concepts of \(k\)-ultrahomogeneity and \(k\)-tuple regularity for finite groups. They are inspired by analogous concepts in graph theory and form natural generalizations of previously known group-theoretic properties such as ultrahomogeneity and automorphism transitivity. In my talk, I will discuss both notions and present a classification result.