Related papers: Metric properties of Baumslag-Solitar groups

We give an exact formula for the number of normal subgroups of each finite index in the Baumslag-Solitar group BS(p,q) when p and q are coprime. Unlike the formula for all finite index subgroups, this one distinguishes different…

This paper gives asymptotic formulas for the subgroup growth and maximal subgroup growth of all Baumslag-Solitar groups.

In this paper we give asymptotics for the conjugacy growth of the soluble Baumslag-Solitar groups $BS(1,k)$, $k\geq 2$, with respect to the standard generating set, by providing a complete description of geodesic conjugacy representatives.…

We introduce the peak normal form of elements of the Baumslag-Solitar groups BS(p,q). This normal form is very close to the length-lexicographical normal form, but more symmetric. Both normal forms are geodesic. This means the normal form…

This paper has two parts, on Baumslag-Solitar groups and on general G-trees. In the first part we establish bounds for stable commutator length (scl) in Baumslag-Solitar groups. For a certain class of elements, we further show that scl is…

We classify the finite-dimensional irreducible linear representations of the Baumslag-Solitar groups BS(p,q) = < a, b | a b^p = b^q a > for relatively prime p and q. The general strategy of the argument is to consider the matrix group given…

A survey of results on the residual properties of Baumslag -- Solitar groups which have been obtained to date.

We exhibit a regular language of geodesics for a large set of elements of $BS(1,n)$ and show that the growth rate of this language is the growth rate of the group. This provides a straightforward calculation of the growth rate of $BS(1,n)$,…

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 prove that for any prime $p\geq 3$ the minimal exponential growth rate of the Baumslag-Solitar group $BS(1,p)$ and the lamplighter group $\mathcal{L}_p=(\mathbb{Z}/p\mathbb{Z})\wr \mathbb{Z}$ are equal. We also show that for $p=2$ this…

We propose a numerical method for studying the cogrowth of finitely presented groups. To validate our numerical results we compare them against the corresponding data from groups whose cogrowth series are known exactly. Further, we add to…

We determine all generalized Baumslag-Solitar groups (finitely generated groups acting on a tree with all stabilizers infinite cyclic) which are quotients of a given Baumslag-Solitar group BS(m,n), and (when BS(m,n) is not Hopfian) which of…

Let $\Gamma=\langle a,b | a b^{p} a^{-1} = b^{q}\rangle$ be a Baumslag--Solitar group and $G$ be a complex reductive algebraic group with maximal compact subgroup $K<G$. We show that, when $p$ and $q$ are relatively prime with distinct…

Any non-residually finite Baumslag-Solitar group has a non-residually finite image in the abstract commensuration of a nonabelian free group. This gives a new proof (avoiding Britton's Lemma) of the classification of residually finite…

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.

We give a parametrization by $m$-adic integers of the limits of Baumslag-Solitar groups (marked with a canonical set of generators). It is shown to be continuous and injective on the invertible $m$-adic integers. We show that all such…

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,…

Let $\rm{Mod(S)}$ be the mapping class group of a closed orientable surface $S$ of genus $g \geq 2$. Let $G$ be a non-elementary subgroup of $\rm{Mod(S)}$ so that the associated Bowen-Margulis measure is finite. In this paper, we give an…

Our main result is that many triangles of Baumslag-Solitar groups collapse to finite groups, generalizing a famous example of Hirsch. A triangle of Baumslag-Solitar groups means a group with three generators, cyclically ordered, with each…

We provide upper bounds for logarithmic torsion homology growth and Betti number growth of groups, phrased in the language of measured group theory.