Explicit strong boundedness for higher rank symplectic groups

Abstract

This paper gives an explicit argument to show strong boundedness for ${\mathrm{Sp}}_{2n}(R)$ for $R$ a ring of S-algebraic integers or a semi-local ring. This gives a quantitative version of a related abstract result in a previous paper of the author. The results presented further generalize older results regarding strong boundedness by Kedra, Libman and Martin and Morris from ${\mathrm{SL}}_n$ to ${\mathrm{Sp}}_{2n}$. Further, the presented results solve the question of the asymptotic of strong boundedness for ${\mathrm{Sp}}_{2n}(R)$ for $R$ semi-local case with an argument that immediately generalizes to all other split Chevalley groups.

Cited by in corpus (3)

• Strong boundedness of simply connected split Chevalley groups defined over rings
• Width of SL(n,O_S,I)
• Strong boundedness of ${\mathrm{SL}}_2(R)$ for rings of S-algebraic integers with infinitely many units