Stability, bounded generation and strong boundedness

Abstract

We provide bounds linear in the rank for the generalized conjugacy diameters, introduced by Kedra, Libman and Martin, for the special linear and symplectic groups defined over the rings of integers of global fields by way of using certain stability considerations familiar from classical algebraic K-theory. This determines the growth rates of these generalized conjugacy diameters.

arXiv commentVersion 3, revised version accepted for publication in the Journal of Topology and Analysis