Presentations for subgroups of Artin groups

  title={Presentations for subgroups of Artin groups},
  author={Warren Dicks and Ian J. Leary},
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. 
Metabelianisations of finitely presented groups
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
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
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
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
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
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
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
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
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
. 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


Morse theory and finiteness properties of groups
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
  • J. Howie
  • Mathematics
    Mathematical 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
Homological dimension of discrete groups
Homological dimension of discrete groups, Queen Mary College Mathematics Notes, University of London
  • 1976