Constructing groups of type $FP_2$ over fields but not over the integers
@inproceedings{Kropholler2021ConstructingGO, title={Constructing groups of type \$FP\_2\$ over fields but not over the integers}, author={Robert P. Kropholler}, year={2021} }
We construct examples of groups that are FP2(Q) and FP2(Z/pZ) for all primes p but not of type FP2(Z).
References
SHOWING 1-10 OF 15 REFERENCES
Subgroups of almost finitely presented groups
- Mathematics
- 2016
We show that every countable group embeds in a group of type $$FP_2$$FP2.
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.
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 3-dimensional special linear groups over integer rings
- Mathematics
- 1992
The following 2-generator 6-relator presentation is obtained for the 3-dimensional special linear group SL(3, Z k ) for each odd integer k>1 : SL(3,Z k )= . Alternative presentations for these groups…
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.
ON THE FINITENESS PROPERTIES OF GROUPS
- Mathematics
- 2013
For an automorphism ' of the group G, the connection between the centralizer CG(') and the commutator (G,') is investigated and as a con- sequence of the Schur theorem it is shown that if G/CG(') and…
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…
Hyperbolic groups with almost finitely presented subgroups
- Mathematics
- 2018
In this paper we create many examples of hyperbolic groups with subgroups satisfying interesting finiteness properties. We give the first examples of subgroups of hyperbolic groups which are of type…
Uncountably many groups of type
- FP . Proc. Lond. Math. Soc
- 2018
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;…