Skip to main content Accessibility help
×
Home

COMPUTING WITH SUBGROUPS OF THE MODULAR GROUP

Published online by Cambridge University Press:  26 August 2014


MARKUS KIRSCHMER
Affiliation:
Lehrstuhl D für Mathematik, RWTH Aachen University, Templergraben 64, 52062 Aachen, Germany e-mail: Markus.Kirschmer@math.rwth-aachen.de
CHARLES LEEDHAM-GREEN
Affiliation:
School of Mathematical Sciences, Queen Mary College University of London, Mile End Road, London E1 4NS, United Kingdom e-mail: C.R.Leedham-Green@qmul.ac.uk

Abstract

We give several algorithms for finitely generated subgroups of the modular group PSL2(ℤ) given by sets of generators. First, we present an algorithm to check whether a finitely generated subgroup H has finite index in the full modular group. Then we discuss how to parametrise the right cosets of H in PSL2(ℤ), whether the index is finite or not. Further, we explain how an element in H can be written as a word in a given set of generators of H.


Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

1.Avenhaus, J. and Madlener, K., The Nielsen reduction and p-complete problems in free groups, Theor. Comput. Sci. 32 (1984), 6176.CrossRefGoogle Scholar
2.Bosma, W., Cannon, J. and Playoust, C., The Magma algebra system. I. The user language, J. Symb. Comput. 24 (3–4) (1997), 235265.CrossRefGoogle Scholar
3.Hsu, T., Identifying congruence subgroups of the modular group, Proc. Amer. Math. Soc. 124 (5) (1996), 13511359.CrossRefGoogle Scholar
4.Karrass, A. and Solitar, D., On finitely generated subgroups of a free group, Proc. Amer. Math. Soc. 22 (1) (1969), 209213.CrossRefGoogle Scholar
5.Lyndon, R. C. and Schupp, P. E., Combinatorial group theory (Springer, New York, NY, 1977).Google Scholar
6.Serre, J.-P., Trees (Springer, New York, NY, 1980).CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 36 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 1st December 2020. This data will be updated every 24 hours.

Access
Hostname: page-component-6d4bddd689-k8xqc Total loading time: 0.543 Render date: 2020-12-01T14:34:15.652Z Query parameters: { "hasAccess": "1", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags last update: Tue Dec 01 2020 13:43:26 GMT+0000 (Coordinated Universal Time) Feature Flags: { "metrics": true, "metricsAbstractViews": false, "peerReview": true, "crossMark": true, "comments": true, "relatedCommentaries": true, "subject": true, "clr": false, "languageSwitch": true }

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

COMPUTING WITH SUBGROUPS OF THE MODULAR GROUP
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

COMPUTING WITH SUBGROUPS OF THE MODULAR GROUP
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

COMPUTING WITH SUBGROUPS OF THE MODULAR GROUP
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *