Explicit generators of some pro-p groups via Bruhat-Tits theory
Group Theory
2017-02-21 v2 Algebraic Geometry
Abstract
Given a semisimple group over a local field of residual characteristic p, its topological group of rational points admits maximal pro-p-subgroups. Quasi-split simply-connected semisimple groups can be described in the combinatorial terms of valued root groups, thanks to Bruhat-Tits theory. In this context, it becomes possible to compute explicitly a minimal generating set of the (all conjugated) maximal pro-p-subgroups thanks to parametrizations of a suitable maximal torus and of corresponding root groups. We show that the minimal number of generators is then linear with respect to the rank of a suitable root system.
Keywords
Cite
@article{arxiv.1701.02194,
title = {Explicit generators of some pro-p groups via Bruhat-Tits theory},
author = {Benoit Loisel},
journal= {arXiv preprint arXiv:1701.02194},
year = {2017}
}