Abstract
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*
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