Related papers: Subgroup growth in free class-$2$-nilpotent groups
We derive a generating series for the number of free subgroups of finite index in $\Delta^+ = \mathbb{Z}_p*\mathbb{Z}_q$ by using a connection between free subgroups of $\Delta^+$ and certain hypermaps (also known as ribbon graphs or "fat"…
The higher rank Lefschetz formula for p-adic groups is used to prove rationality of a several-variable zeta function attached to the action of a p-adic group on its Bruhat-Tits building. By specializing to certain lines one gets…
Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…
We recall the relation between Zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of Zeta…
Two groups are said to have the same nilpotent genus if they have the same nilpotent quotients. We answer four questions of Baumslag concerning nilpotent completions. (i) There exists a pair of finitely generated, residually…
We show that every effectively closed action of a finitely generated group $G$ on a closed subset of $\{0,1\}^{\mathbb{N}}$ can be obtained as a topological factor of the $G$-subaction of a $(G \times H_1 \times H_2)$-subshift of finite…
We develop a refinement of Whitehead's algorithm for primitive words in a free group. We generalize to subgroups, establishing a strengthened version of Whitehead's algorithm for free factors. We make use of these refinements in proving new…
We develop an algorithm that computes strongly continuous semigroups on infinite-dimensional Hilbert spaces with explicit error control. Given a generator $A$, a time $t>0$, an arbitrary initial vector $u_0$ and an error tolerance…
We discuss in the context of finite extensions two classical theorems of Takahasi and Howson on subgroups of free groups. We provide bounds for the rank of the intersection of subgroups within classes of groups such as virtually free…
We introduce the notion of an EZ-structure on a group. Delta-hyperbolic groups and CAT(0)-groups have EZ-structures. We show torsion-free groups having an EZ-structure automatically have an action by homeomorphisms on a closed…
A new definition for the Riemann zeta function for all positive integer number s > 1 is presented. We discover a most elegant expression and easy method for calculating the Riemann zeta function for small even integer values. Through this…
Given an endomorphism $\varphi: G \to G$ on a group $G$, one can define the Reidemeister number $R(\varphi) \in \mathbb{N} \cup \{\infty\}$ as the number of twisted conjugacy classes. The corresponding Reidemeister zeta function…
The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of…
Given a finitely generated, torsion-free nilpotent group, we find the maximum possible (critical) regularity for its faithful actions by diffeomorphisms of the closed or half-open interval and of the circle. Our result gives an expression…
In this paper, we provide an effective method to compute the topological entropies of $G$-subshifts of finite type ($G$-SFTs) with $G=F_{d}$ and $S_{d}$, the free group and free semigroup with $d$ generators respectively. We develop the…
We construct an efficient model for graphs of finitely generated subgroups of free groups. Using this we give a very short proof of Dicks's reformulation of the strengthened Hanna Neumann Conjecture as the Amalgamated Graph Conjecture. In…
We give a length one projective resolution of the trivial module for the groupoid of a semi-saturated partial action (in the sense of Exel) of a free group on a compact Hausdorff and totally disconnected space. As a consequence we obtain an…
Let $\Gamma$ be a finite graph, and for each vertex $i$ let $G_i$ be a finitely presented group. Let $G$ be the graph product of the $G_i$. That is, $G$ is the group obtained from the free product of the $G_i$ by factoring out by the…
We define the class of groups of bounded type from tile inflations. These tile inflations also determine some automata describing the groups. In the case when the automata are stationary, we show that if the set of incompressible elements…
We discuss a method of calculating the zeta function of subshifts which have a presentation by a finite directed graph labeled by elements of the associated inverse semigroup. This class of subshifts is introduced as a class of property A…