2021/08/27 by Alexander A. Trost, Trost, Alexander A.
Computer Science · Mathematics · #20G30 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2108.12254
openalex publication_date 2021/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bounded generation by root elements is a property which has been widely\nstudied for various types of linear algebraic groups defined over rings of\nintegers in algebraic number fields. However, when considering global function\nfields, there are not many results beyond the treatment of special cases due to\nNica and Queen. In this paper, we use model theoretic methods due to Carter,\nKeller and Paige written up by Morris to prove bounded generation by root\nelements for simply connected, split Chevalley groups defined over the ring of\nall integers in a global function field. We further apply this bounded\ngeneration result together with results from a previous paper by the author to\nderive that the aforementioned Chevalley groups satisfy the strong boundedness\nproperty introduced by Kedra, Libman and Martin.\n