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arXiv · 2309.04083

Short words of infinite order

Junho Peter Whang
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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.

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Junho Peter Whang. 2023-09-08. Short words of infinite order. https://arxiv.org/abs/2309.04083

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