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Uniform bounded elementary generation of Chevalley groups
- Part of
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- Journal:
- Canadian Journal of Mathematics , First View
- Published online by Cambridge University Press:
- 10 December 2024, pp. 1-28
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- Article
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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.
