2023/09/08 by Junho Peter Whang, Whang, Junho Peter
Computer Science · Mathematics · #20G25 #22E40 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2309.04083
openalex publication_date 2023/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an infinite linear group with a finite set of generators, we show that the shortest word length of an element of infinite order has an upper bound that depends only on the number of generators and the degree. This provides a quantification of the Burnside problem for linear groups. In degree two, an explicit bound is computed using an exceptional connection to reflection groups.