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.
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
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
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
• Mathematics
Inventiones 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
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
On the virtual and residual properties of a generalization of Bestvina-Brady groups
• Mathematics
• 2022
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)

References

SHOWING 1-10 OF 12 REFERENCES
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
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
Cohomology of Groups
This advanced textbook introduces students to cohomology theory. No knowledge of homological algebra is assumed beyond what is normally taught in a first course in algebraic topology.
Combinatorial Group Theory
• Mathematics
• 1977
Chapter I. Free Groups and Their Subgroups 1. Introduction 2. Nielsen's Method 3. Subgroups of Free Groups 4. Automorphisms of Free Groups 5. Stabilizers in Aut(F) 6. Equations over Groups 7.
Embedding Theorems for Groups
• Mathematics
Proceedings of the Edinburgh Mathematical Society
• 1962
By a partial endomorphism of a group G we mean a homomorphic mapping μ of a subgroup A of G onto a subgroup B of G. If μ is denned on the whole of G then it is called a total endomorphism. We call a
Almost finitely presented soluble groups
• Mathematics
• 1978
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