相关论文: Free-by-cyclic groups, automorphisms and actions o…

We prove that ascending HNN extensions of free groups are word-hyperbolic if and only if they have no Baumslag-Solitar subgroups. This extends the theorem of Brinkmann that free-by-cyclic groups are word-hyperbolic if and only if they have…

We study the Fibered Isomorphism conjecture of Farrell and Jones for groups acting on trees. We show that under certain conditions the conjecture is true for groups acting on trees when the stabilizers satisfy the conjecture. These…

Given an automorphism of a free group $F_n$, we consider the following invariants: $e$ is the number of exponential strata (an upper bound for the number of different exponential growth rates of conjugacy classes); $d$ is the maximal degree…

We give necessary and sufficient conditions for a free-by-free group to be relatively hyperbolic with a cusp-preserving structure. Namely, if $\phi_1, \ldots , \phi_k $ is a collection of exponentially growing outer automorphisms with a…

We give a geometric description of the Poisson boundaries of certain extensions of free and hyperbolic groups. In particular, we get a full description of the Poisson boundaries of free-by-cyclic groups. We rely upon the description of…

Almost-direct products of free groups arise naturally in braid theory and in the study of automorphism groups of free groups. Although bi-invariant orderings are known to exist for many such groups, their explicit structure is often left…

The paper concerns the automorphism groups of Cayley graphs over cyclic groups which have a rational spectrum (rational circulant graphs for short). With the aid of the techniques of Schur rings it is shown that the problem is equivalent to…

For $\beta\in{\mathbb Z}$, let $G(\beta)=\langle A,B\,|\, A^{[A,B]}=A,\, B^{[B,A]}=B^\beta\rangle$ be the infinite Macdonald group, and set $C=[A,B]$. Then $G(\beta)$ is a nilpotent polycyclic group of the form $\langle…

Let T be a tree with an action of a finitely generated group G. Given a suitable equivalence relation on the set of edge stabilizers of T (such as commensurability, co-elementarity in a relatively hyperbolic group, or commutation in a…

We compute explicitly the automorphism and outer automorphism group of all large-type free-of-infinity Artin groups. Our strategy involves reconstructing the associated Deligne complexes in a purely algebraic manner, i.e. in a way that is…

Let $\Phi:F\rightarrow F$ be an automorphism of the finite-rank free group $F$. Suppose that $G=F\rtimes_\Phi\mathbb Z$ is word-hyperbolic. Then $G$ acts freely and cocompactly on a CAT(0) cube complex.

Let $G$ be a torsion-free hyperbolic group and $\alpha$ an automorphism of $G$. We show that there exists a canonical collection of subgroups that are polynomially growing under $\alpha$, and that the mapping torus of $G$ by $\alpha$ is…

We provide new examples of acylindrically hyperbolic groups arising from actions on simplicial trees. In particular, we consider amalgamated products and HNN-extensions, 1-relator groups, automorphism groups of polynomial algebras,…

We prove that for a free product $G$ with free factor system $\mathcal{G}$, any automorphism $\phi$ preserving $\mathcal{G}$, atoroidal (in a sense relative to $\mathcal{G}$) and none of whose power send two different conjugates of…

We extend Forester's rigidity theorem so as to give a complete characterization of rigid group actions on trees (an action is rigid if it is the only reduced action in its deformation space, in particular it is invariant under automorphisms…

We construct, for the free group acting on its Cayley tree, boomerang subgroups whose critical exponent is arbitrarily close to the critical exponent of a given finitely generated subgroup.

We study biinvariant word metrics on groups. We provide an efficient algorithm for computing the biinvariant word norm on a finitely generated free group and we construct an isometric embedding of a locally compact tree into the biinvariant…

A subset $S$ of a group $G$ invariably generates $G$ if $G$ is generated by $\{ s^g(s) | s\in S\} $ for any choice of $g(s)\in G, s\in S$. In case $G$ is topological one defines similarly the notion of topological invariable generation. A…

We start by studying the distribution of (cyclically reduced) elements of the free groups Fn with respect to their abelianization (or equivalently, their integer homology class. We derive an explicit generating function, and a limiting…

We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm…