A note concerning Fox's paper on Fenchel's conjecture
Author: T. C. Chau
Journal: Proc. Amer. Math. Soc. 88 (1983), 584-586
MSC: Primary 20F05; Secondary 20B27, 20H10
MathSciNet review: 702279
Abstract: The object of this note is to point out and correct an error in the paper  of Fox, purporting to prove Fenchel's conjecture that a finitely generated, infinite Fuchsian group has a torsion-free normal subgroup of finite index. Fox divided the proof of the main result in his paper into four cases and an error occurs in the proofs of Cases (III) and (IV). A direct proof of Case (III) was given. While a direct proof of Case (IV) can be given, the author shows that it also follows indirectly from the result in the paper  of Burns and Solitar.
-  R. G. Burns and Donald Solitar, The indices of torsion-free subgroups of Fuchsian groups, Proc. Amer. Math. Soc. 89 (1983), no. 3, 414–418. MR 715855, https://doi.org/10.1090/S0002-9939-1983-0715855-0
-  Ralph H. Fox, On Fenchel’s conjecture about 𝐹-groups, Mat. Tidsskr. B. 1952 (1952), 61–65. MR 0053937