Geodesic
On a Result of A. M. Macbeath on Normal Subgroups of a Fuchsian Group
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 15-16

Voir la notice de l'article provenant de la source Cambridge University Press

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 * 
Jonsson, W. On a Result of A. M. Macbeath on Normal Subgroups of a Fuchsian Group. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 15-16. doi: 10.4153/CMB-1970-003-0
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