New uniform diameter bounds in pro-$p$ groups
Accepted version
Peer-reviewed
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Repository DOI
Change log
Authors
Bradford, Henry https://orcid.org/0000-0003-2949-8095
Abstract
We give new upper bounds for the diameters of finite groups which do not depend on a choice of generating set. Our method exploits the commutator structure of certain profinite groups, in a fashion analogous to the Solovay–Kitaev procedure from quantum computation. We obtain polylogarithmic upper bounds for the diameters of finite quotients of groups with an analytic structure over a pro-p domain (with exponent depending on the dimension); Chevalley groups over a pro-p domain (with exponent independent of the dimension) and the Nottingham group of a finite field. We also discuss some consequences of our results for random walks on groups.
Description
Keywords
4904 Pure Mathematics, 49 Mathematical Sciences
Journal Title
Groups, Geometry, and Dynamics
Conference Name
Journal ISSN
1661-7207
1661-7215
1661-7215
Volume Title
12
Publisher
European Mathematical Society - EMS - Publishing House GmbH
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All rights reserved