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On a Result of A. M. Macbeath on Normal Subgroups of a Fuchsian Group

Published online by Cambridge University Press:  20 November 2018

W. Jonsson*
Affiliation:
McGill University, Montreal, Quebec
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A. M. Macbeath, in November 1965, communicated the following theorem to me which he proved with the aid of the Lefschetz fixed point formula.

Theorem. If Γ is a Fuchsian group and N a torsion free normal subgroup, then the rank of N/[Γ, N] is twice the genus of the orbit space D/Γ where D denotes the hyperbolic plane which Γ acts.

This theorem will follow from a consideration of the exact sequence

*

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1970

References

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4. Sah, C. H., Groups related to compact Rieman surfaces, Acta Math. 123 (1969), 13-42.Google Scholar