Year: 2023
Type: preprint
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 $Φ$ of rank $\ge 2$ there exists a universal bound $L=L(Φ)$ such that the simply connected Chevalley groups $G(Φ,R)$ have elementary width $\le L$ for all Dedekind rings of arithmetic type $R$.
Source: arXiv (Cornell University)
Authors: Kunyavskii, Boris, Plotkin, Eugene, Vavilov, Nikolai
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Israel Science Foundation
Award: G6611866667
OpenAlex ID: W4385473454