Explicit generators of some pro-p groups via Bruhat-Tits theory

Benoit Loisel (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Domaines: Théorie des groupes [math.GR]; Géométrie algébrique [math.AG]

Benoit Loisel. Explicit generators of some pro-p groups via Bruhat-Tits theory. 2017. ⟨hal-01428864v1⟩