Uniform bounded elementary generation of Chevalley groups

2023/07/28 by Boris Kunyavskiı̆, Eugene Plotkin, Kunyavskii, Boris +3
Mathematics · #20G07 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2307.15756

openalex publication_date 2023/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we establish a definitive result which almost completely closes the problem of bounded elementary generation for Chevalley groups of rank ≥ 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 ≥ 2 there exists a universal bound L=L(Φ) such that the simply connected Chevalley groups G(Φ,R) have elementary width ≤ L for all Dedekind rings of arithmetic type R.

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