# 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} }

We show that every countable group embeds in a group of type $$FP_2$$FP2.

## 6 Citations

### Groups of type $FP$ via graphical small cancellation

- Mathematics
- 2020

We construct an uncountable family of groups of type $FP$. In contrast to every previous construction of non-finitely presented groups of type $FP$ we do not use Morse theory on cubical complexes;…

### 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…

### Constructing groups of type $FP_2$ over fields but not over the integers

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We construct examples of groups that are FP2(Q) and FP2(Z/pZ) for all primes p but not of type FP2(Z).

### Simple groups separated by finiteness properties

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We show that for every positive integer n there exists a simple group that is of type $$\mathrm {F}_{n-1}$$Fn-1 but not of type $$\mathrm {F}_n$$Fn. For $$n\ge 3$$n≥3 these groups are the first known…

### Profinite rigidity of fibring

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- 2022

. 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

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- 2022

Previously one of us introduced a family of groups G ML ( 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 G…

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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…

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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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A rink-type roller skate is provided with a plastic sole plate. To mount a toe stop on the skate, a novel bushing is embedded in the sole plate. The bushing has relatively small diameter ends and a…

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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.