Related papers: Convergence of Baumslag-Solitar groups

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 prove that for any natural n>1, the abstract commensurator group of the Baumslag - Solitar group BS(1,n) is isomorphic to the group of 2 by 2 upper triangular matrices A over rational numbers with A_{11}=1. We also prove that for any…

We give an affirmative answer to the Grunwald problem for new families of non-solvable finite groups G, away from the set of primes dividing |G|. Furthermore, we show that such G verify the condition (BM), that is, the Brauer-Manin…

For a Baumslag-Solitar group $G$ we calculate the intersection $\gamma_w(G)$ of all terms of the lower central sequence of $G$.Using this we are able to show that $[\gamma_w(G),G]=\gamma_w(G)$ thus answering a question of Bardakov and…

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…

Let $\Gamma$ be the fundamental group of a surface of finite type and Comm$(\Gamma)$ be its abstract commensurator. Then Comm$(\Gamma)$ contains the solvable Baumslag--Solitar groups $\langle a ,b : a b a^{-1} = b^n \rangle$ for any $n >…

An A-infinity bialgebra of type (m,n) is a Hopf algebra H equipped with a "compatible" operation \omega : H^{\otimes m} \to H^{\otimes n} of positive degree. We determine the structure relations for A-infinity bialgebras of type (m,n) and…

We show that if a group contains $\mathbb{Z}^n \times F_m$ as a finite-index subgroup, then its cogrowth series is the diagonal of a rational function for every generating set. This answers a question of Pak and Soukup on the cogrowth of…

The problem of embedding an ample semigroup in an inverse semigroup as a (2, 1, 1)-type subalgebra is known to be undecidable. In this article, we investigate the problem for certain classes of ample semigroups. We also give examples of…

This paper studies automatic structures for subsemigroups of Baumslag--Solitar semigroups (that is, semigroups presented by $\ < x,y \mid (yx^m, x^ny)\ >$, where $m$ and $n$ are natural numbers). A geometric argument (a rarity in the field…

Every sequence of orbifolds corresponding to pairwise non-conjugate congruence lattices in a higher rank semisimple group over local fields of zero characteristic is Benjamini--Schramm convergent to the universal cover.

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 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…

We give a short argument showing that if $m, n \in {1, 2, ...} \cup {\omega}$, then the groups mV and nV are not isomorphic. This answers a question of Brin.

The Stein group $F_{2,3}$ is the group of orientation-preserving homeomorphisms of the unit interval with slopes of the form $2^p3^q$ ($p,q\in\mathbb{Z}$) and breakpoints in $\mathbb{Z}[\frac{1}{6}]$. This is a natural relative of…

We show that Baumslag-Solitar groups are virtually 2-avoidable, that is, they admit finite index subgroup whose first homology is devoid of $\mathbb{Z}_2$ summand. We also prove virtual 2-avoidability for some other classes of one-relator…

The Baumslag-Solitar groups and their certain variations are a-T-menable. This is proved by embeding them into topological groups and studying representation theoretic properties of the latter. The paper is motivated by the questions of A.…

In this paper we explore the interplay between aspects of the geometry and algebra of three families of groups of the form B semidirect the integers Z, namely Lamplighter groups, solvable Baumslag-Solitar groups and lattices in SOL. In…

We prove that one-relator groups are coherent, solving a well-known problem of Gilbert Baumslag. Our proof strategy is readily applicable to many classes of groups of cohomological dimension two. We show that fundamental groups of…

The set of automorphisms of a one-dimensional \shift $(X, \sigma)$ forms a countable, but often very complicated, group. For zero entropy shifts, it has recently been shown that the automorphism group is more tame. We provide the first…