• Corpus ID: 232068943

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
Groups of type $FP$ via graphical small cancellation
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;
Presentations for subgroups of Artin groups
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
Subgroups of almost finitely presented groups
We show that every countable group embeds in a group of type $$FP_2$$FP2.
Morse theory and finiteness properties of groups
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
Presentations for 3-dimensional special linear groups over integer rings
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
Abstract. We construct continuously many quasiisometry classes of torsion-free 2-generator small cancellation groups.
ON THE FINITENESS PROPERTIES OF GROUPS
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
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
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
...
...