Short words of infinite order
Group Theory
2023-09-11 v1 Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2309.04083,
title = {Short words of infinite order},
author = {Junho Peter Whang},
journal= {arXiv preprint arXiv:2309.04083},
year = {2023}
}
Comments
14 pages. Comments are welcome!