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

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.**Robert Bieri,*Homological dimension of discrete groups*, Mathematics Department, Queen Mary College, London, 1976. Queen Mary College Mathematics Notes. MR**0466344****3.**I. M. Chiswell,*The Euler characteristic of graph products and of Coxeter groups*, Discrete groups and geometry (Birmingham, 1991) London Math. Soc. Lecture Note Ser., vol. 173, Cambridge Univ. Press, Cambridge, 1992, pp. 36–46. MR**1196914**, 10.1017/CBO9780511565793.006**4.**P. M. Cohn and Warren Dicks,*On central extensions of skew fields*, J. Algebra**63**(1980), no. 1, 143–151. MR**568568**, 10.1016/0021-8693(80)90029-0**5.**Carl Droms,*Subgroups of graph groups*, J. Algebra**110**(1987), no. 2, 519–522. MR**910401**, 10.1016/0021-8693(87)90063-9**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**(1980), no. 2, 179–186. MR**567067**, 10.1016/0022-4049(80)90083-3**8.**John Stallings,*A finitely presented group whose 3-dimensional integral homology is not finitely generated*, Amer. J. Math.**85**(1963), 541–543. MR**0158917**

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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:
http://dx.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