# Groups of type $FP$ via graphical small cancellation

@article{Brown2020GroupsOT, title={Groups of type \$FP\$ via graphical small cancellation}, author={Thomas A. G. Brown and Ian J. Leary}, journal={arXiv: Group Theory}, year={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; instead we use Gromov's graphical small cancellation theory.

## 2 Citations

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

- Mathematics
- 2021

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

### Profinite rigidity of fibring

- Mathematics
- 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…

## References

SHOWING 1-10 OF 35 REFERENCES

### 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…

### Presentations for subgroups of Artin groups

- Mathematics
- 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…

### Morse theory and finiteness properties of groups

- Mathematics
- 1997

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.

### Subgroups of almost finitely presented groups

- Mathematics
- 2016

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

### Uncountably many quasi-isometry classes of groups of type FP

- MathematicsAmerican Journal of Mathematics
- 2020

Abstract:In an earlier paper, one of the authors constructed uncountable families of groups of type $FP$ and of $n$-dimensional Poincar\\'e duality groups for each $n\\geq 4$. We show that those…

### On a small cancellation theorem of Gromov

- Mathematics
- 2003

We give a combinatorial proof of a theorem of Gromov, which extends the scope of small cancellation theory to group presentations arising from labelled graphs.

### Branched Coverings of Cubical Complexes and Subgroups of Hyperbolic Groups

- Mathematics
- 1999

By considering branched coverings of piecewise Euclidean cubical complexes, the paper provides an example of a torsion free hyperbolic group containing a finitely presented subgroup which is not…

### Groups with graphical C(6) and C(7) small cancellation presentations

- Mathematics
- 2012

We extend fundamental results of small cancellation theory to groups whose presentations satisfy the generalizations of the classical C(6) and C(7) conditions in graphical small cancellation theory.…

### Continuously many quasiisometry classes of 2-generator groups

- Mathematics
- 1998

Abstract. We construct continuously many quasiisometry classes of torsion-free 2-generator small cancellation groups.

### Simple groups separated by finiteness properties

- MathematicsInventiones mathematicae
- 2018

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…