Related papers: On fixed points and stabilizers in solvable Baumsl…

For any algebraically closed field $K$ and any endomorphism $f$ of $\mathbb{P}^1(K)$ of degree at least 2, the automorphisms of $f$ are the M\"obius transformations that commute with $f$, and these form a finite subgroup of…

In this article we study automorphisms and endomorphisms of lacunary hyperbolic groups. We prove that every lacunary hyperbolic group is Hopfian, answering a question by Henry Wilton. In addition, we show that if a lacunary hyperbolic group…

An original non-standard approach to describing the structure of a column stabilizer in a group of $n \times n$ matrices over a polynomial ring or a Laurent polynomial ring of $n$ variables is presented. The stabilizer is described as an…

A group, $\fl{H}$, of automorphisms of a totally disconnected locally compact group, $G$, is flat if there is a compact open $U\leq G$ such that the index $[\alpha(U):U\cap \alpha(U)]$ is mininimized for every $\alpha\in\fl{H}$. The…

We consider the action of outer automorphisms on the deformation space $\mathcal{O}$ of $G$-trees given by a free product decomposition of a group $G$. We show that an irreducible, displacement 1 automorphism fixes exactly one point in…

In this article, we study the space of subgroups of non-amenable generalized Baumslag-Solitar groups (GBS groups) of rank $d$, that is, groups acting cocompactly on an oriented tree with vertex and edge stabilizers isomorphic to…

Inspired by the techniques of Givental and Th\'eret, we provide a proof with generating functions of a recent result of Ginzburg-G\"urel concerning the periodic points of Hamiltonian diffeomorphisms of $\mathbb{C}\text{P}^d$. For instance,…

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 determine all finite p-groups that admit a faithful, self-similar action on the p-ary rooted tree such that the first level stabilizer is abelian. A group is in this class if and only if it is a split extension of an elementary abelian…

Given a group $G$ with bounded torsion that acts properly on a systolic complex, we show that every solvable subgroup of $G$ is finitely generated and virtually abelian of rank at most $2$. In particular this gives a new proof of the above…

We determine the structure of automorphism groups of finite graphs of bounded Hadwiger number. Our proof includes a structural analysis of finite edge-transitive graphs. In particular, we show that for connected, $K_{h+1}$-minor-free,…

We provide polynomial lower bounds for residual finiteness of residually finite, finitely generated solvable groups that admit infinite order elements in the Fitting subgroup of strict distortion at least exponential. For this class of…

We obtain conditions of uniform continuity for endomorphisms of free-abelian times free groups for the product metric defined by taking the prefix metric in each component and establish an equivalence between uniform continuity for this…

Let $G\curvearrowright T$ be a minimal action on an $\mathbb{R}$--tree with $G$ finitely presented. Assuming that $G$ is accessible over the family of arc-stabilisers of $T$, we give a description of the point-stabilisers of $T$ in terms of…

The group Diff(S^1) of the orientation preserving diffeomorphisms of the circle S^1 plays an important role in conformal field theory. We consider a subgroup B_0 of Diff(S^1) whose elements stabilize "the point of infinity". This subgroup…

Let $\Bbbk$ be a perfect field with algebraic closure $\overline{\Bbbk}$. If $H$ is a subgroup of plane automorphisms over $\Bbbk$ and $p\in\overline{\Bbbk}^2$ is a point, we describe the subgroup consisting of plane automorphisms which…

We prove that if $\F$ is an abelian group of $C^1$ diffeomorphisms isotopic to the identity of a closed surface $S$ of genus at least two then there is a common fixed point for all elements of $\F.$

In 1993, Muzychuk \cite{muzychuk} showed that the rational Schur rings over a cyclic group $Z_n$ are in one-to-one correspondence with sublattices of the divisor lattice of $n$, or equivalently, with sublattices of the lattice of subgroups…

We look at constructions of aperiodic SFTs on fundamental groups of graph of groups. In particular we prove that all generalized Baumslag-Solitar groups (GBS) admit a strongly aperiodic SFT. Our proof is based on a structural theorem by…

In analogy with the free factors of a free group we define special factors of Generalized Baumslag-Solitar (GBS) groups as non-cyclic subgroups which appear in splittings over infinite cyclic groups. We give an algorithm which, given a GBS…