JournalsggdVol. 12, No. 3pp. 803–836

New uniform diameter bounds in pro-pp groups

  • Henry Bradford

    Georg-August-Universität Göttingen Germany
New uniform diameter bounds in pro-$p$ groups cover
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Abstract

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-pp domain (with exponent depending on the dimension); Chevalley groups over a pro-pp 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.

Cite this article

Henry Bradford, New uniform diameter bounds in pro-pp groups. Groups Geom. Dyn. 12 (2018), no. 3, pp. 803–836

DOI 10.4171/GGD/457