Subgroups of almost finitely presented groups

@article{Leary2016SubgroupsOA,
  title={Subgroups of almost finitely presented groups},
  author={Ian J. Leary},
  journal={Mathematische Annalen},
  year={2016},
  volume={372},
  pages={1383-1391}
}
  • I. Leary
  • Published 18 October 2016
  • Mathematics
  • Mathematische Annalen
We show that every countable group embeds in a group of type $$FP_2$$FP2. 
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6 Citations
Background Citations
1
Methods Citations
1

6 Citations

Groups of type $FP$ via graphical small cancellation
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Constructing groups of type $FP_2$ over fields but not over the integers
We construct examples of groups that are FP2(Q) and FP2(Z/pZ) for all primes p but not of type FP2(Z).
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Profinite rigidity of fibring
. We introduce the classes of TAP groups, in which various types of algebraic fibring are detected by the non-vanishing of twisted Alexander polynomials. We show that finitely presented LERF groups lie…
On the virtual and residual properties of a generalization of Bestvina-Brady groups
Previously one of us introduced a family of groups GL (S), parametrized by a finite flag complex L, a regular covering M of L, and a set S of integers. We give conjectural descriptions of when GL (S)…

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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.
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…
Subgroups of finitely presented groups
  • G. Higman
  • Mathematics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1961
The main theorem of this paper states that a finitely generated group can be embedded in a finitely presented group if and only if it has a recursively enumerable set of defining relations. It…
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1.1 Finitely presented soluble groups have been investigated by several authors. Roughly speaking, their results deal with two aspects: with the subgroup structure of finitely presented soluble…
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