Bounded generation and commutator width of Chevalley groups: function case

Autor:	Kunyavskii, Boris, Plotkin, Eugene, Vavilov, Nikolai
Rok vydání:	2022
Předmět:	Mathematics - Group Theory 20G07 Structure theory for linear algebraic groups
Druh dokumentu:	Working Paper
Popis:	We prove that Chevalley groups over polynomial rings $\mathbb F_q[t]$ and over Laurent polynomial $\mathbb F_q[t,t^{-1}]$ rings, where $\mathbb F_q$ is a finite field, are boundedly elementarily generated. Using this we produce explicit bounds of the commutator width of these groups. Under some additional assumptions, we prove similar results for other classes of Chevalley groups over Dedekind rings of arithmetic rings in positive characteristic. As a corollary, we produce explicit estimates for the commutator width of affine Kac--Moody groups defined over finite fields. The paper contains also a broader discussion of the bounded generation problem for groups of Lie type, some applications and a list of unsolved problems in the field. Comment: 54 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2204.10951 Zobrazit plný text záznamu View this record from Arxiv