---
_id: '42801'
abstract:
- lang: eng
  text: We exhibit a practical algorithm for solving the constructive membership problem
    for discrete free subgroups of rank 2 in PSL₂(R) or SL₂(R). This algorithm, together
    with methods for checking whether a two-generator subgroup of PSL₂(R) or SL₂(R)
    is discrete and free, have been implemented in Magma for groups defined over real
    algebraic number fields.
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
- first_name: CHARLES
  full_name: LEEDHAM-GREEN, CHARLES
  last_name: LEEDHAM-GREEN
citation:
  ama: Kirschmer M, LEEDHAM-GREEN C. Computing with subgroups of the modular group
    . <i>Glasgow Mathematical Journal</i>. 2014;57(1):173-180. doi:<a href="https://doi.org/10.1017/s0017089514000202">10.1017/s0017089514000202</a>
  apa: Kirschmer, M., &#38; LEEDHAM-GREEN, C. (2014). Computing with subgroups of
    the modular group . <i>Glasgow Mathematical Journal</i>, <i>57</i>(1), 173–180.
    <a href="https://doi.org/10.1017/s0017089514000202">https://doi.org/10.1017/s0017089514000202</a>
  bibtex: '@article{Kirschmer_LEEDHAM-GREEN_2014, title={Computing with subgroups
    of the modular group }, volume={57}, DOI={<a href="https://doi.org/10.1017/s0017089514000202">10.1017/s0017089514000202</a>},
    number={1}, journal={Glasgow Mathematical Journal}, publisher={Cambridge University
    Press (CUP)}, author={Kirschmer, Markus and LEEDHAM-GREEN, CHARLES}, year={2014},
    pages={173–180} }'
  chicago: 'Kirschmer, Markus, and CHARLES LEEDHAM-GREEN. “Computing with Subgroups
    of the Modular Group .” <i>Glasgow Mathematical Journal</i> 57, no. 1 (2014):
    173–80. <a href="https://doi.org/10.1017/s0017089514000202">https://doi.org/10.1017/s0017089514000202</a>.'
  ieee: 'M. Kirschmer and C. LEEDHAM-GREEN, “Computing with subgroups of the modular
    group ,” <i>Glasgow Mathematical Journal</i>, vol. 57, no. 1, pp. 173–180, 2014,
    doi: <a href="https://doi.org/10.1017/s0017089514000202">10.1017/s0017089514000202</a>.'
  mla: Kirschmer, Markus, and CHARLES LEEDHAM-GREEN. “Computing with Subgroups of
    the Modular Group .” <i>Glasgow Mathematical Journal</i>, vol. 57, no. 1, Cambridge
    University Press (CUP), 2014, pp. 173–80, doi:<a href="https://doi.org/10.1017/s0017089514000202">10.1017/s0017089514000202</a>.
  short: M. Kirschmer, C. LEEDHAM-GREEN, Glasgow Mathematical Journal 57 (2014) 173–180.
date_created: 2023-03-07T08:47:42Z
date_updated: 2023-04-04T07:55:16Z
department:
- _id: '102'
doi: 10.1017/s0017089514000202
extern: '1'
intvolume: '        57'
issue: '1'
keyword:
- General Mathematics
language:
- iso: eng
page: 173-180
publication: Glasgow Mathematical Journal
publication_identifier:
  issn:
  - 0017-0895
  - 1469-509X
publication_status: published
publisher: Cambridge University Press (CUP)
status: public
title: 'Computing with subgroups of the modular group '
type: journal_article
user_id: '93826'
volume: 57
year: '2014'
...
---
_id: '64685'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Ultrametric and non-locally convex analogues of the general curve
    Lemma of convenient differential calculus. <i>Glasgow Mathematical Journal</i>.
    2008;50(2):271–288. doi:<a href="https://doi.org/10.1017/S0017089508004199">10.1017/S0017089508004199</a>
  apa: Glöckner, H. (2008). Ultrametric and non-locally convex analogues of the general
    curve Lemma of convenient differential calculus. <i>Glasgow Mathematical Journal</i>,
    <i>50</i>(2), 271–288. <a href="https://doi.org/10.1017/S0017089508004199">https://doi.org/10.1017/S0017089508004199</a>
  bibtex: '@article{Glöckner_2008, title={Ultrametric and non-locally convex analogues
    of the general curve Lemma of convenient differential calculus}, volume={50},
    DOI={<a href="https://doi.org/10.1017/S0017089508004199">10.1017/S0017089508004199</a>},
    number={2}, journal={Glasgow Mathematical Journal}, author={Glöckner, Helge},
    year={2008}, pages={271–288} }'
  chicago: 'Glöckner, Helge. “Ultrametric and Non-Locally Convex Analogues of the
    General Curve Lemma of Convenient Differential Calculus.” <i>Glasgow Mathematical
    Journal</i> 50, no. 2 (2008): 271–288. <a href="https://doi.org/10.1017/S0017089508004199">https://doi.org/10.1017/S0017089508004199</a>.'
  ieee: 'H. Glöckner, “Ultrametric and non-locally convex analogues of the general
    curve Lemma of convenient differential calculus,” <i>Glasgow Mathematical Journal</i>,
    vol. 50, no. 2, pp. 271–288, 2008, doi: <a href="https://doi.org/10.1017/S0017089508004199">10.1017/S0017089508004199</a>.'
  mla: Glöckner, Helge. “Ultrametric and Non-Locally Convex Analogues of the General
    Curve Lemma of Convenient Differential Calculus.” <i>Glasgow Mathematical Journal</i>,
    vol. 50, no. 2, 2008, pp. 271–288, doi:<a href="https://doi.org/10.1017/S0017089508004199">10.1017/S0017089508004199</a>.
  short: H. Glöckner, Glasgow Mathematical Journal 50 (2008) 271–288.
date_created: 2026-02-26T11:22:06Z
date_updated: 2026-02-27T08:19:56Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1017/S0017089508004199
intvolume: '        50'
issue: '2'
keyword:
- '26E15'
- '26E20'
- '26E30'
- 46A16
- 46S10
language:
- iso: eng
page: 271–288
publication: Glasgow Mathematical Journal
publication_identifier:
  issn:
  - 0017-0895
quality_controlled: '1'
status: public
title: Ultrametric and non-locally convex analogues of the general curve Lemma of
  convenient differential calculus
type: journal_article
user_id: '178'
volume: 50
year: '2008'
...
---
_id: '64701'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Contraction groups for tidy automorphisms of totally disconnected
    groups. <i>Glasgow Mathematical Journal</i>. 2005;47(2):329–333. doi:<a href="https://doi.org/10.1017/S0017089505002557">10.1017/S0017089505002557</a>
  apa: Glöckner, H. (2005). Contraction groups for tidy automorphisms of totally disconnected
    groups. <i>Glasgow Mathematical Journal</i>, <i>47</i>(2), 329–333. <a href="https://doi.org/10.1017/S0017089505002557">https://doi.org/10.1017/S0017089505002557</a>
  bibtex: '@article{Glöckner_2005, title={Contraction groups for tidy automorphisms
    of totally disconnected groups}, volume={47}, DOI={<a href="https://doi.org/10.1017/S0017089505002557">10.1017/S0017089505002557</a>},
    number={2}, journal={Glasgow Mathematical Journal}, author={Glöckner, Helge},
    year={2005}, pages={329–333} }'
  chicago: 'Glöckner, Helge. “Contraction Groups for Tidy Automorphisms of Totally
    Disconnected Groups.” <i>Glasgow Mathematical Journal</i> 47, no. 2 (2005): 329–333.
    <a href="https://doi.org/10.1017/S0017089505002557">https://doi.org/10.1017/S0017089505002557</a>.'
  ieee: 'H. Glöckner, “Contraction groups for tidy automorphisms of totally disconnected
    groups,” <i>Glasgow Mathematical Journal</i>, vol. 47, no. 2, pp. 329–333, 2005,
    doi: <a href="https://doi.org/10.1017/S0017089505002557">10.1017/S0017089505002557</a>.'
  mla: Glöckner, Helge. “Contraction Groups for Tidy Automorphisms of Totally Disconnected
    Groups.” <i>Glasgow Mathematical Journal</i>, vol. 47, no. 2, 2005, pp. 329–333,
    doi:<a href="https://doi.org/10.1017/S0017089505002557">10.1017/S0017089505002557</a>.
  short: H. Glöckner, Glasgow Mathematical Journal 47 (2005) 329–333.
date_created: 2026-02-26T12:02:52Z
date_updated: 2026-02-27T07:56:02Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1017/S0017089505002557
extern: '1'
intvolume: '        47'
issue: '2'
keyword:
- 22D05
- 22D40
- 22D45
language:
- iso: eng
page: 329–333
publication: Glasgow Mathematical Journal
publication_identifier:
  issn:
  - 0017-0895
quality_controlled: '1'
status: public
title: Contraction groups for tidy automorphisms of totally disconnected groups
type: journal_article
user_id: '178'
volume: 47
year: '2005'
...
---
_id: '64718'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Approximation by p-adic Lie groups. <i>Glasgow Mathematical Journal</i>.
    2002;44(2):231–239. doi:<a href="https://doi.org/10.1017/S0017089502020049">10.1017/S0017089502020049</a>
  apa: Glöckner, H. (2002). Approximation by p-adic Lie groups. <i>Glasgow Mathematical
    Journal</i>, <i>44</i>(2), 231–239. <a href="https://doi.org/10.1017/S0017089502020049">https://doi.org/10.1017/S0017089502020049</a>
  bibtex: '@article{Glöckner_2002, title={Approximation by p-adic Lie groups}, volume={44},
    DOI={<a href="https://doi.org/10.1017/S0017089502020049">10.1017/S0017089502020049</a>},
    number={2}, journal={Glasgow Mathematical Journal}, author={Glöckner, Helge},
    year={2002}, pages={231–239} }'
  chicago: 'Glöckner, Helge. “Approximation by P-Adic Lie Groups.” <i>Glasgow Mathematical
    Journal</i> 44, no. 2 (2002): 231–239. <a href="https://doi.org/10.1017/S0017089502020049">https://doi.org/10.1017/S0017089502020049</a>.'
  ieee: 'H. Glöckner, “Approximation by p-adic Lie groups,” <i>Glasgow Mathematical
    Journal</i>, vol. 44, no. 2, pp. 231–239, 2002, doi: <a href="https://doi.org/10.1017/S0017089502020049">10.1017/S0017089502020049</a>.'
  mla: Glöckner, Helge. “Approximation by P-Adic Lie Groups.” <i>Glasgow Mathematical
    Journal</i>, vol. 44, no. 2, 2002, pp. 231–239, doi:<a href="https://doi.org/10.1017/S0017089502020049">10.1017/S0017089502020049</a>.
  short: H. Glöckner, Glasgow Mathematical Journal 44 (2002) 231–239.
date_created: 2026-02-26T12:26:19Z
date_updated: 2026-02-27T07:43:12Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1017/S0017089502020049
extern: '1'
intvolume: '        44'
issue: '2'
keyword:
- 22D05
- '22E50'
- '20E26'
- 14L10
language:
- iso: eng
page: 231–239
publication: Glasgow Mathematical Journal
publication_identifier:
  issn:
  - 0017-0895
quality_controlled: '1'
status: public
title: Approximation by p-adic Lie groups
type: journal_article
user_id: '178'
volume: 44
year: '2002'
...