Upper bounds on the number of conjugacy classes in unitriangular groups

Abstract

We provide a new upper bound on the number of conjugacy classes in the group $U_n(q)$ of unitriangular matrices over a finite field. We also compute a similar upper bound for every group in the lower central series of $U_n(q)$.

arXiv comment26 pages; v2 -- Major rewrite, including improved upper bounds and expanded exposition