The hunt for regular orbits of almost quasisimple groups

The hunt for regular orbits of almost quasisimple groups

 Let G be a permutation group on Omega. We say that G has a regular orbit on Omega if there exists x in Omega that is fixed only by the identity permutation.

Regular orbits arise in a number of applications including the study of Frobenius groups and the proof of the celebrated k(GV)-theorem, which gives an upper bound on the number of conjugacy classes of certain affine groups where |G| and |V| are coprime.

One of the major cases in the proof of the k(GV)-theorem was a study of regular orbits of the so-called almost quasisimple groups G (i.e., G/F(G) is an almost simple group).

In this talk, after giving some background and motivation, Dr Lee will discuss progress in her quest to finish classifying all pairs (G,V) where G is an almost quasisimple group with a regular orbit on its irreducible module $V$. By the proof of the k(GV)-problem, this boils down to the cases where (|G|,|V|) >1. She will also briefly discuss techniques used for this classification, which involve some algebraic group theory, character theory and computational methods.

 Speaker

Dr Melissa Lee, University of Auckland

How to attend 

If not a member of the Dept. Mathematical Science at the University of Essex, you can register your interest in attending the seminar and request the Zoom’s meeting password by emailing Dr Jesus Martinez-Garcia.