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

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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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