---
_id: '64691'
abstract:
- lang: eng
  text: We show that countable direct limits of finite-dimensional Lie groups do not
    have small subgroups. The same conclusion is obtained for suitable direct limits
    of infinite-dimensional Lie groups.
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Direct limit groups do not have small subgroups. <i>Topology and
    its Applications</i>. 2007;154(6):1126-1133. doi:<a href="https://doi.org/10.1016/j.topol.2006.11.003">https://doi.org/10.1016/j.topol.2006.11.003</a>
  apa: Glöckner, H. (2007). Direct limit groups do not have small subgroups. <i>Topology
    and Its Applications</i>, <i>154</i>(6), 1126–1133. <a href="https://doi.org/10.1016/j.topol.2006.11.003">https://doi.org/10.1016/j.topol.2006.11.003</a>
  bibtex: '@article{Glöckner_2007, title={Direct limit groups do not have small subgroups},
    volume={154}, DOI={<a href="https://doi.org/10.1016/j.topol.2006.11.003">https://doi.org/10.1016/j.topol.2006.11.003</a>},
    number={6}, journal={Topology and its Applications}, author={Glöckner, Helge},
    year={2007}, pages={1126–1133} }'
  chicago: 'Glöckner, Helge. “Direct Limit Groups Do Not Have Small Subgroups.” <i>Topology
    and Its Applications</i> 154, no. 6 (2007): 1126–33. <a href="https://doi.org/10.1016/j.topol.2006.11.003">https://doi.org/10.1016/j.topol.2006.11.003</a>.'
  ieee: 'H. Glöckner, “Direct limit groups do not have small subgroups,” <i>Topology
    and its Applications</i>, vol. 154, no. 6, pp. 1126–1133, 2007, doi: <a href="https://doi.org/10.1016/j.topol.2006.11.003">https://doi.org/10.1016/j.topol.2006.11.003</a>.'
  mla: Glöckner, Helge. “Direct Limit Groups Do Not Have Small Subgroups.” <i>Topology
    and Its Applications</i>, vol. 154, no. 6, 2007, pp. 1126–33, doi:<a href="https://doi.org/10.1016/j.topol.2006.11.003">https://doi.org/10.1016/j.topol.2006.11.003</a>.
  short: H. Glöckner, Topology and Its Applications 154 (2007) 1126–1133.
date_created: 2026-02-26T11:43:06Z
date_updated: 2026-02-26T11:44:04Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: https://doi.org/10.1016/j.topol.2006.11.003
extern: '1'
intvolume: '       154'
issue: '6'
keyword:
- Infinite-dimensional Lie group
- Direct limit group
- Direct limit
- Inductive limit
- Small subgroup
- Torsion subgroup
language:
- iso: eng
page: 1126-1133
publication: Topology and its Applications
publication_identifier:
  issn:
  - 0166-8641
quality_controlled: '1'
status: public
title: Direct limit groups do not have small subgroups
type: journal_article
user_id: '178'
volume: 154
year: '2007'
...