In this event organised by Women in Mathematical Sciences at Lund, we have a PhD student from the University of Geneva. This talk will assume knowledge of undergraduate group theory.

Title: Crown-based powers and their applications

Abstract: Initially discovered by Gaschutz in the 1950s, before later being extended by Dalla Volta and Lucchini in the 1990s, the theory of crowns in finite groups has a long and rich history, with numerous applications. Central to this theory is the observation that establishing generation results for a particular class of groups, known as crown-based powers, is often sufficient to derive corresponding results for all finite groups. In this talk, we will explore how this framework can be applied to a range of generation problems, highlighting in particular how the structure of a group’s chief factors determines its generation behaviour.