Geodesic
New uniform diameter bounds in pro-$p$ groups
Henry Bradford1 orcid
1Georg-August-Universität Göttingen Germany
Groups, geometry, and dynamics, Tome 12 (2018) no. 3, pp. 803-836

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DOI

We give newupper 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.
DOI : 10.4171/ggd/457
Classification : 20-XX, 05-XX
Mots-clés : Analytic pro-p groups, diameters, spectral gap

Henry Bradford  1

1 Georg-August-Universität Göttingen Germany 
Henry Bradford. New uniform diameter bounds in pro-$p$ groups. Groups, geometry, and dynamics, Tome 12 (2018) no. 3, pp. 803-836. doi: 10.4171/ggd/457
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     doi = {10.4171/ggd/457},
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