Presentations for subgroups of Artin groups

Authors:
Warren Dicks and Ian J. Leary

Journal:
Proc. Amer. Math. Soc. **127** (1999), 343-348

MSC (1991):
Primary 20F36; Secondary 20E07, 20F32

DOI:
https://doi.org/10.1090/S0002-9939-99-04873-X

MathSciNet review:
1605948

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Abstract | References | Similar Articles | Additional Information

Abstract: Recently, M. Bestvina and N. Brady have exhibited groups that are of type but not finitely presented. We give explicit presentations for groups of the type considered by Bestvina-Brady. This leads to algebraic proofs of some of their results.

**1.**M. Bestvina and N. Brady, Morse theory and finiteness properties of groups, to appear in Invent. Math.**2.**R. Bieri, Homological dimension of discrete groups, Queen Mary College Mathematics Notes, University of London (1976). MR**57:6224****3.**I. M. Chiswell, The Euler characteristic of graph products and of Coxeter groups, Discrete groups and Geometry (Birmingham 1991), London Math. Soc. Lecture Notes 173, 36-46, Cambridge Univ. Press, Cambridge (1992). MR**94a:05090****4.**W. Dicks, An exact sequence for rings of polynomials in partly commuting indeterminates, J. Pure Appl. Algebra 22, 215-228 (1981). MR**82m:16014****5.**C. Droms, Subgroups of graph groups, J. Algebra 110, 519-522 (1987). MR**88m:05046****6.**J. Howie, Bestvina-Brady groups and the plus construction, preprint (1997).**7.**K. H. Kim and F. W. Roush, Homology of certain algebras defined by graphs, J. Pure Appl. Algebra 17, 179-186 (1980). MR**82e:05114b****8.**J. R. Stallings, A finitely presented group whose 3-dimensional integral homology is not finitely generated, Amer. J. Math. 85, 541-543 (1963). MR**28:2139**

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Additional Information

**Warren Dicks**

Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra (Barcelona), Spain

Email:
dicks@manwe.mat.uab.es

**Ian J. Leary**

Affiliation:
Faculty of Mathematical Studies, University of Southampton, Southampton, SO17 1BJ, United Kingdom

Email:
ijl@maths.soton.ac.uk

DOI:
https://doi.org/10.1090/S0002-9939-99-04873-X

Keywords:
Artin group,
presentation

Received by editor(s):
May 17, 1997

Additional Notes:
W. Dicks acknowledges support from the DGICYT (Spain) through grant number PB93-0900

I. Leary acknowledges support from the Nuffield Foundation through grant number SCI/180/96/127, and from EPSRC grant number GR/L06928

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1999
American Mathematical Society