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COMPUTING WITH SUBGROUPS OF THE MODULAR GROUP

Published online by Cambridge University Press:  26 August 2014

MARKUS KIRSCHMER  and
CHARLES LEEDHAM-GREEN
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
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Abstract

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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.

Keywords

20-0420H05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 1 , January 2015 , pp. 173 - 180
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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