---
_id: '63569'
abstract:
- lang: eng
  text: "Let $G$ be a totally disconnected locally compact (tdlc) group. The contraction
    group $\\mathrm{con}(g)$ of an element $g\\in G$ is the set of all $h\\in G$ such
    that $g^n h g^{-n} \\to 1_G$ as $n \\to \\infty$. The nub of $g$ can then be characterized
    as the intersection $\\mathrm{nub}(g)$ of the closures of $\\mathrm{con}(g)$ and
    $\\mathrm{con}(g^{-1})$.\r\n Contraction groups and nubs provide important tools
    in the study of the structure of tdlc groups, as already evidenced in the work
    of G. Willis. It is known that $\\mathrm{nub}(g) = \\{1\\}$ if and only if $\\mathrm{con}(g)$
    is closed. In general, contraction groups are not closed and computing the nub
    is typically a challenging problem.\r\n Maximal Kac-Moody groups over finite fields
    form a prominent family of non-discrete compactly generated simple tdlc groups.
    In this paper we give a complete description of the nub of any element in these
    groups."
author:
- first_name: Sebastian
  full_name: Bischof, Sebastian
  id: '106729'
  last_name: Bischof
- first_name: Timothée
  full_name: Marquis, Timothée
  last_name: Marquis
citation:
  ama: Bischof S, Marquis T. Describing the nub in maximal Kac-Moody groups. Published
    online 2025.
  apa: Bischof, S., &#38; Marquis, T. (2025). <i>Describing the nub in maximal Kac-Moody
    groups</i>.
  bibtex: '@article{Bischof_Marquis_2025, title={Describing the nub in maximal Kac-Moody
    groups}, author={Bischof, Sebastian and Marquis, Timothée}, year={2025} }'
  chicago: Bischof, Sebastian, and Timothée Marquis. “Describing the Nub in Maximal
    Kac-Moody Groups,” 2025.
  ieee: S. Bischof and T. Marquis, “Describing the nub in maximal Kac-Moody groups.”
    2025.
  mla: Bischof, Sebastian, and Timothée Marquis. <i>Describing the Nub in Maximal
    Kac-Moody Groups</i>. 2025.
  short: S. Bischof, T. Marquis, (2025).
date_created: 2026-01-12T14:12:09Z
date_updated: 2026-01-12T14:33:08Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
  arxiv:
  - arXiv:2508.15506
language:
- iso: eng
status: public
title: Describing the nub in maximal Kac-Moody groups
type: preprint
user_id: '106729'
year: '2025'
...
---
_id: '63568'
abstract:
- lang: eng
  text: In this article we work out the details of flat groups of the automorphism
    group of locally finite Bruhat-Tits buildings.
author:
- first_name: Sebastian
  full_name: Bischof, Sebastian
  id: '106729'
  last_name: Bischof
citation:
  ama: Bischof S. On flat groups in affine buildings. Published online 2025.
  apa: Bischof, S. (2025). <i>On flat groups in affine buildings</i>.
  bibtex: '@article{Bischof_2025, title={On flat groups in affine buildings}, author={Bischof,
    Sebastian}, year={2025} }'
  chicago: Bischof, Sebastian. “On Flat Groups in Affine Buildings,” 2025.
  ieee: S. Bischof, “On flat groups in affine buildings.” 2025.
  mla: Bischof, Sebastian. <i>On Flat Groups in Affine Buildings</i>. 2025.
  short: S. Bischof, (2025).
date_created: 2026-01-12T14:11:47Z
date_updated: 2026-01-12T14:32:33Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
  arxiv:
  - arXiv:2512.16548
language:
- iso: eng
status: public
title: On flat groups in affine buildings
type: preprint
user_id: '106729'
year: '2025'
...