Related papers: The isomorphism problem for small-rose generalized…
Generalized Baumslag-Solitar groups (GBS groups) are groups that act on trees with infinite cyclic edge and vertex stabilizers. Such an action is described by a labeled graph (essentially, the quotient graph of groups). This paper addresses…
We prove that the isomorphism problem is decidable for generalized Baumslag-Solitar (GBS) groups with one quasi-conjugacy class and full support gaps. In order to do so we introduce a family of invariants that fully characterize the…
A generalized Baumslag-Solitar (GBS) group is a finitely generated group acting on a tree with infinite cyclic edge and vertex stabilizers. We show how to determine effectively the rank (minimal cardinality of a generating set) of a GBS…
We study the structure of generalized Baumslag-Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of…
A generalized Baumslag-Solitar group (GBS group) is a finitely generated group $G$ which acts on a tree with all edge and vertex stabilizers infinite cyclic. We show that Out(G) either contains non-abelian free groups or is virtually…
In this paper we classify Baumslag-Solitar groups up to commensurability. In order to prove our main result we give a solution to the isomorphism problem for a subclass of Generalised Baumslag-Solitar groups.
The Baumslag-Solitar groups: BS(m,n)=<x,y| x y^{m} x^{-1} = y^{n}> are some of the simplest interesting infinite groups which are not lattices in Lie groups. They have been studied in depth from the point of view of combinatorial group…
We introduce a new isomorphism invariant for generalized Baumslag-Solitar (GBS) groups, which we call the limit angle. Unlike previously known invariants, which are primarily algebraic, the limit angle admits a dynamical interpretation,…
A generalized Baumslag-Solitar group is the fundamental group of a graph of groups all of whose vertex and edge groups are infinite cyclic. Levitt proves that any generalized Baumslag-Solitar group has property R-infinity, that is, any…
We investigate fixed subgroups of automorphisms of generalised Baumslag-Solitar (GBS) groups. Our main results are for automorphisms leaving a Bass-Serre tree invariant, under the assumption that all edge stabilisers are strictly contained…
We introduce two new moves on graphs of groups with cyclic edge groups that preserve the fundamental group. These moves allow us to address the isomorphism problem without the use of expansions, therefore keeping the number of vertices and…
A rank $n$ generalized Baumslag-Solitar group is a group that splits as a finite graph of groups such that all vertex and edge groups are isomorphic to $\mathbb{Z}^n$. In this paper we classify these groups in terms of their separability…
In this note we characterise all finitely generated groups elementarily equivalent to a solvable Baumslag-Solitar group BS$(1,n)$. It turns out that a finitely generated group $G$ is elementarily equivalent to BS$(1,n)$ if and only if $G$…
We characterize when a generalized Baumslag-Solitar group is linear, and extend the result to the fundamental groups of a graph of groups with infinite virtually cyclic vertex and edge groups.
The solvable Baumslag Solitar groups $\text{BS}(1,n)$ each admit a canonical model space, $X_n$. We give a complete classification of lattices in $G_n = \text{Isom}^+(X_n)$ and find that such lattices fail to be strongly…
A finitely generated group $G$ acting on a tree with infinite cyclic edge and vertex stabilizers is called a generalized Baumslag--Solitar group ($GBS$ group). We prove that a 1-knot group $G$ is $GBS$ group iff $G$ is a torus-knot group…
We show that all residually finite generalized Baumslag-Solitar groups of rank $n \geq 1$, defined on a finite and connected graph, are self-similar. Furthermore we prove that all residually finite fundamental groups of (finite, connected)…
Generalized Baumslag-Solitar groups are defined as fundamental groups of graphs of groups with infinite cyclic vertex and edge groups. Forester proved (in "On uniqueness of JSJ decompositions of finitely generated groups", Comment. Math.…
We look at isometric actions on arbitrary hyperbolic spaces of generalised Baumslag - Solitar groups of arbitrary dimension (the rank of the free abelian vertex and edge subgroups). It is known that being a hierarchically hyperbolic group…
In this article, we study the space of subgroups of generalized Baumslag-Solitar groups (GBS groups), that is, groups acting cocompactly on an oriented tree without inversion and with infinite cyclic vertex and edge stabilizers. Our results…