  In this paper we establish a definitive result which almost completely closes
the problem of bounded elementary generation for Chevalley groups of rank $\ge
2$ over arbitrary Dedekind rings $R$ of arithmetic type, with uniform bounds.
Namely, we show that for every reduced irreducible root system $\Phi$ of rank
$\ge 2$ there exists a universal bound $L=L(\Phi)$ such that the simply
connected Chevalley groups $G(\Phi,R)$ have elementary width $\le L$ for all
Dedekind rings of arithmetic type $R$. For symplectic groups this result is new
even in the number case.

Group Theory