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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: [email protected]
CHARLES LEEDHAM-GREEN
Affiliation:
School of Mathematical Sciences, Queen Mary College University of London, Mile End Road, London E1 4NS, United Kingdom e-mail: [email protected]
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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

REFERENCES

1.Avenhaus, J. and Madlener, K., The Nielsen reduction and p-complete problems in free groups, Theor. Comput. Sci. 32 (1984), 61–76.Google Scholar
2.Bosma, W., Cannon, J. and Playoust, C., The Magma algebra system. I. The user language, J. Symb. Comput. 24 (3–4) (1997), 235–265.Google Scholar
3.Hsu, T., Identifying congruence subgroups of the modular group, Proc. Amer. Math. Soc. 124 (5) (1996), 1351–1359.Google Scholar
4.Karrass, A. and Solitar, D., On finitely generated subgroups of a free group, Proc. Amer. Math. Soc. 22 (1) (1969), 209–213.Google 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