Related papers: On Tame Subgroups of Finitely Presented Groups
Let $G$ be the fundamental group of a finite graph of groups with Noetherian edges and locally tame vertices. We prove that $G$ is locally tame. It follows that if a finitely presented group $H$ has a non-trivial $JSJ$-decomposition over…
We give two examples of a finitely generated subgroup of a free group and a subset, closed in the profinite topology of a free group, such that their product is not closed in the profinite topology of a free group.
Let $p$ be a prime number, and let $k$ be an algebraically closed field of characteristic $p$. We show that the tame fundamental group of a smooth affine curve over $k$ is a projective profinite group. We prove that the fundamental group of…
We present examples of closed subsets of a free group such that their product is not closed in the profinite topology. We discuss how to characterize a subset of a free group which is closed in the profinite topology and its product with…
It is proved that all finitely generated subgroups of generalized free product of two groups are finitely separable provided that free factors have this property and amalgamated subgroups are normal in corresponding factors and satisfy the…
A new pair of asymptotic invariants for finitely presented groups, called intrinsic and extrinsic tame filling functions, are introduced. These filling functions are quasi-isometry invariants that strengthen the notions of intrinsic and…
We determine derived representation type of complete finitely generated local and two-point algebras over an algebraically closed field.
We investigate the structure of subdirect products of groups, particularly their finiteness properties. We pay special attention to the subdirect products of free groups, surface groups and HNN extensions. We prove that a finitely presented…
We establish a general criterion for the finite presentability of subdirect products of groups and use this to characterize finitely presented residually free groups. We prove that, for all $n\in\mathbb{N}$, a residually free group is of…
We say that a finitely generated group $\Gamma$ is self-simulable if every effectively closed action of $\Gamma$ on a closed subset of $\{\texttt{0},\texttt{1}\}^{\mathbb{N}}$ is the topological factor of a $\Gamma$-subshift of finite type.…
It is shown that a closed solvable subgroup of a connected Lie group is compactly generated. In particular, every discrete solvable subgroup of a connected Lie group is finitely generated. Generalizations to locally compact groups are…
We show that on an arbitrary finitely generated non virtually solvable linear group, any two independent random walks will eventually generate a free subgroup. In fact, this will hold for an exponential number of independent random walks.
A result of Baumslag and Roseblade states that a finitely presented subgroup of the direct product of two free groups is virtually a direct product of free groups. In this paper we generalise this result to the class of cyclic subgroup…
We prove that, in characteristic zero, closed subgroups of the polynomial automorphisms group containing the affine group contain the whole tame group.
We determine all the ways in which a direct product of two finite groups can be expressed as the set-theoretical union of proper subgroups in a family of minimal cardinality.
It is known that in any free group the isolator of finitely generated subgroup is finitely generated subgroup. A very simple proof of this statement is proposed.
The goal of this article is to study results and examples concerning finitely presented covers of finitely generated amenable groups. We collect examples of groups $G$ with the following properties: (i) $G$ is finitely generated, (ii) $G$…
We prove that it is decidable whether or not a finitely generated submonoid of a virtually free group is graded, introduce a new geometric characterization as quasi-geodesic monoids, and show that their word problem is rational (as a…
A remarkable result of Thompson states that a finite group is soluble if and only if its two-generated subgroups are soluble. This result has been generalized in numerous ways, and it is in the core of a wide area of research in the theory…
We establish representation types (finite, tame or wild) of finite dimensional Munn algebras with semisimple bases. As an application, we establish representation types of finite 0-simple semigroups and their mutually annihilating unions.