New uniform diameter bounds in pro- p groups

作者：Bradford Henry^*

来源：Groups, Geometry, and Dynamics, 2018, 12(3): 803-836.

DOI：10.4171/GGD/457

• Analytic pro- p groups
• diameters
• spectral gap

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.

• 出版日期2018