Explicit strong boundedness for higher rank symplectic groups

Abstract

This paper gives an explicit argument to show strong boundedness for Sp2n(R) for R a ring of S-algebraic integers or a semi-local ring thereby giving a quantitative version of the abstract result in the paper [15]. The results presented further generalize older results regarding strong boundedness by Kedra, Libman and Martin [6] and Morris [9] from SLn to Sp2n. The results also completely solve the question of the asymptotic of strong boundedness for Sp2n(R) for R semi-local case with an argument that immediately generalizes to all other split Chevalley groups.