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

DOI10.24033/BSMF.2831arXiv1701.02194MaRDI QIDQ6281696

Publication date: 9 January 2017

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.

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Groups with a (BN)-pair; buildings (20E42) Linear algebraic groups over local fields and their integers (20G25) Limits, profinite groups (20E18) Root systems (17B22)

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