Geodesic
A Generalization of Lyndon's Theorem on the Cohomology of One-Relator Groups
Canadian journal of mathematics, Tome 28 (1976) no. 3, pp. 473-480

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

In this paper we generalize a theorem of Lyndon's [7], which states that a one-relator group G = F/(r) (F is free and r Ç F) has cohomological dimension cd (F/(r)) ≧ 2 if and only if the relator r is not a proper power in F. His proof relies on the Identity Theorem and recently he has shown [8] how a generalized version of this theorem and a generalized version of the Freiheitsatz can be simultaneously obtained by the methods of combinatorial geometry. These generalizations refer to a situation where the free group F is replaced by a free product of subgroups of the additive group of real numbers. 
Gildenhuys, D. A Generalization of Lyndon's Theorem on the Cohomology of One-Relator Groups. Canadian journal of mathematics, Tome 28 (1976) no. 3, pp. 473-480. doi: 10.4153/CJM-1976-048-6
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