The Normal Subgroup Theorem for lattices on two-dimensional Euclidean buildings
Group Theory
2026-05-08 v1 Dynamical Systems
Abstract
We prove the normal subgroup property for every group that acts properly and cocompactly on a two-dimensional Euclidean building: every normal subgroup has finite index or is contained in the finite kernel of the action. As a consequence, the non-residually finite lattices constructed by Titz Mite and the second author are virtually simple. They are the first known simple lattices on irreducible Euclidean buildings.
Cite
@article{arxiv.2605.06163,
title = {The Normal Subgroup Theorem for lattices on two-dimensional Euclidean buildings},
author = {Jean Lécureux and Stefan Witzel},
journal= {arXiv preprint arXiv:2605.06163},
year = {2026}
}
Comments
74 pages, 4 figures