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arXiv · 2307.15756

Uniform bounded elementary generation of Chevalley groups

Boris Kunyavskii·Eugene Plotkin·Nikolai Vavilov
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Abstract

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 $R$.

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Boris Kunyavskii, Eugene Plotkin, Nikolai Vavilov. 2023-07-28. Uniform bounded elementary generation of Chevalley groups. https://arxiv.org/abs/2307.15756

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