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A Generalization of Lyndon's Theorem on the Cohomology of One-Relator Groups

Published online by Cambridge University Press:  20 November 2018

D. Gildenhuys
D. Gildenhuys*
Affiliation:
McGill University, Montreal, Quebec
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 3 , 01 June 1976 , pp. 473 - 480
Copyright
Copyright © Canadian Mathematical Society 1976

References

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