The Normal Subgroup Theorem for lattices on two-dimensional Euclidean buildings
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913098763337728 |
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| author | Lécureux, Jean Witzel, Stefan |
| author_facet | Lécureux, Jean Witzel, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06163 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Normal Subgroup Theorem for lattices on two-dimensional Euclidean buildings Lécureux, Jean Witzel, Stefan Group Theory Dynamical Systems 22E40, 11F06, 20E07, 20F65, 43A85, 51E24 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. |
| title | The Normal Subgroup Theorem for lattices on two-dimensional Euclidean buildings |
| topic | Group Theory Dynamical Systems 22E40, 11F06, 20E07, 20F65, 43A85, 51E24 |
| url | https://arxiv.org/abs/2605.06163 |