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Presentations for subgroups of Artin groups
Author(s):
Warren
Dicks;
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:
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.
References:
- 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:
10.1090/S0002-9939-99-04873-X
PII:
S 0002-9939(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
Copyright of article:
Copyright
1999,
American Mathematical Society
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