A Generalization of Lyndon's Theorem on the Cohomology of One-Relator Groups
- 1 June 1976
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 28 (3) , 473-480
- https://doi.org/10.4153/cjm-1976-048-6
Abstract
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.Keywords
This publication has 1 reference indexed in Scilit:
- Homology and standard constructionsPublished by Springer Nature ,1969