# Presentations for subgroups of Artin groups

@inproceedings{Dicks1999PresentationsFS, title={Presentations for subgroups of Artin groups}, author={Warren Dicks and Ian J. Leary}, year={1999} }

Recently, M. Bestvina and N. Brady have exhibited groups that are of type FP 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.

## 44 Citations

Metabelianisations of finitely presented groups

- Mathematics
- 2018

In this article, I study some classes of finitely presented groups with the aim of finding out whether the maximal metabelian quotients of the members of these classes admit finite presentations. The…

Isomorphisms Between Bestsvina--Brady Groups and Right-angled Artin Groups

- Mathematics
- 2020

We give a combinatorial criterion for determining which Bestvina--Brady group is isomorphic to a right-angled Artin group.

Abelian Splittings and JSJ-Decompositions of Bestvina--Brady Groups

- Mathematics
- 2020

We give a characterization of Bestvina--Brady groups split over abelian subgroups and describe a JSJ-decomposition of Bestvina--Brady groups.

Bounded Rank Subgroups of Coxeter Groups, Artin Groups and One‐Relator Groups with Torsion

- Mathematics
- 2002

We obtain a number of results regarding the freeness of subgroups of Coxeter groups, Artin groups and one‐relator groups with torsion. In the case of Coxeter groups, we also obtain results on…

Uncountably many groups of type FP

- Mathematics
- 2015

We construct uncountably many discrete groups of type FP; in particular we construct groups of type FP that do not embed in any finitely presented group. We compute the ordinary, ℓ2 , and compactly…

Bestvina--Brady Groups with Polynomial Dehn Functions

- Mathematics
- 2019

Let $\Gamma$ be a finite simplicial graph that contains no induced $K_{4}$ subgraphs. We show that with some assumptions, the Dehn function of the associated Bestvina--Brady group is polynomial.

Arrangements of hypersurfaces and Bestvina–Brady groups

- Mathematics
- 2015

We show that quasi-projective Bestvina-Brady groups are fundamental groups of complements to hyperplane arrangements. Furthermore we relate other normal subgroups of right-angled Artin groups to…

THE !-COHOMOLOGY OF ARTIN GROUPS

- Mathematics
- 2002

For each Artin group, the reduced !2-cohomology of (the universal cover of) its ‘Salvetti complex’ is computed. This is a CW-complex which is conjectured to be a model for the classifying space of…

Algebraic invariants for Bestvina–Brady groups

- Mathematics
- 2007

Bestvina–Brady groups arise as kernels of length homomorphisms GΓ → ℤ from right‐angled Artin groups to the integers. Under some connectivity assumptions on the flag complex ΔΓ, we compute several…

A note on torsion length and torsion subgroups

- Mathematics
- 2021

. Answering Questions 19.23 and 19.24 from the Kourovka notebook we construct polycyclic groups with arbitrary torsion lengths and give examples of ﬁnitely presented groups whose quotients by their…

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Abstract. We examine the finiteness properties of certain subgroups of “right angled” Artin groups. In particular, we find an example of a group that is of type FP(Z) but is not finitely presented.

Bestvina–Brady groups and the plus construction

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1999

A recent result of Bestvina and Brady [1, theorem 8·7], shows that one of two outstanding questions has a negative answer; either there exists a group of cohomological dimension 2 and geometric…

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