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arXiv · 2605.06163

The Normal Subgroup Theorem for lattices on two-dimensional Euclidean buildings

Jean Lécureux·Stefan Witzel
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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.

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Jean Lécureux, Stefan Witzel. 2026-05-07. The Normal Subgroup Theorem for lattices on two-dimensional Euclidean buildings. https://arxiv.org/abs/2605.06163

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