On the number of conjugacy classes of a permutation group

Let $G$ be a subgroup of $S_n$. What can be said on the number of conjugacy classes of $G$, in terms of $n$?

I will review many results from the literature and give examples. I will then present an upper bound for the case where $G$ is primitive with nonabelian socle. This states that either $G$ belongs to explicit families of examples, or the number of conjugacy classes is smaller than $n/2$, and in fact, it is $o(n)$. I will finish with a few questions. Joint work with Nick Gill. 

 

Date and Venue

Start Date
Venue
Online seminar
End Date

Speaker

Daniele Garzoni

Speaker's Institution

Tel Aviv University

Files

Area

Algebra, Combinatorics and Number Theory