Work

Uniform bounded elementary generation of Chevalley groups

Year: 2024

Type: article

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 .

Source: Canadian Journal of Mathematics

DOI: 10.4153/s0008414x24000713

Authors: Boris Kunyavskiı̆, Eugene Plotkin, Nikolai Vavilov

Institutions: Bar-Ilan University, St Petersburg University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450

Funder: Israel Science Foundation