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Torsion free groups generated by a pair of rational parabolic Möbius transformations

Published online by Cambridge University Press:  17 April 2009

John Bamberg  and
Grant Cairns
John Bamberg
Affiliation:
School of Mathematics, La Trobe University, Melbourne Vic 3083, Australia, e-mail: jbaml@students.latrobe.edu.auG.Cairns@latrobe.edu.au
Grant Cairns
Affiliation:
School of Mathematics, La Trobe University, Melbourne Vic 3083, Australia, e-mail: jbaml@students.latrobe.edu.auG.Cairns@latrobe.edu.au
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Abstract

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Let T be a subgroup of PSL (2, ℚ) generated by a pair of rational parabolic matrices P1, P2, and let ℐ be the Jøgensen number. We prove that T has a non-trivial element of finite order if and only if ℐ = 4/n2 or ℐ = 9/n2 for some non-zero integer n.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 1 , February 2000 , pp. 151 - 152
Copyright
Copyright © Australian Mathematical Society 2000

References

REFERENCES

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