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PSL(2, q) as an image of the extended modular group with applications to group actions on surfaces

Published online by Cambridge University Press:  20 January 2009

David Singerman
David Singerman
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO9 5NH
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The modular group PSL(2, ℤ), which is isomorphic to a free product of a cyclicgroupof order 2 and a cyclic group of order 3, has many important homomorphic images. Inparticular, Macbeath [7] showed that PSL(2, q) is an image of the modular group if q ≠ 9. (Here, as usual, q is a prime power.) The extended modular group PGL(2, ℤ) contains PSL{2, ℤ) with index 2. It has a presentation

the subgroup PSL(2, ℤ) being generated by UV and VW.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 1 , February 1987 , pp. 143 - 151
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

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