---
_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'
...