Related papers: Limits of dihedral groups

We describe the two-generated limits of abelian-by-(infinite cyclic) groups in the space of marked groups using number theoretic methods. We also discuss universal equivalence of these limits.

In the space of marked group, we determine the structure of groups which are limit points of the set of all generalized quaternion groups.

We give a topological framework for the study of Sela's limit groups: limit groups are limits of free groups in a compact space of marked groups. Many results get a natural interpretation in this setting. The class of limit groups is known…

In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.

In this paper we obtain significant bounds for the number of maximal subgroups of a given index of a finite group. These results allow us to give new bounds for the number of random generators needed to generate a finite $d$-generated group…

We prove that Hausdorff limit of topological minimal sets (with finitely generated coefficient group) are topologically minimal. The key idea is to reduce the homology group on the space to the homology group on the sphere, and reduce the…

In this paper, we introduce the t-graphs defined on finitely-generate groups. We study some general aspects of the t-graphs on 2-generator groups, emphasising establishing necessary conditions for their connectedness. In particular, we…

We consider a few types of bounded homomorphisms on a topological group. These classes of bounded homomorphisms are, in a sense, weaker than the class of continuous homomorphisms. We show that with appropriate topologies each class of these…

We classify the metric spaces that can be approximated by finite homogeneous ones.

We prove that any finitely generated one ended group has linear end depth. Moreover, we give alternative proofs to theorems relating the growth of a finitely generated group to the number of its ends.

We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups.

We consider the problem of realizing a group as the fundamental group of a graph of groups where the vertex groups are restricted to certain classes (for example, coming from a certain finite list of groups, or having bounded geometric…

Some boundedness properties of function spaces (considered as topological groups) are studied.

We describe structure of locally finite groups of finite centraliser dimension.

Let $\mathcal G$ denote the space of finitely generated marked groups. For any finitely generated group $G$, we construct a continuous, injective map $f$ from the space of subgroups $Sub(G)$ to $\mathcal G$ that sends conjugate subgroups to…

Surface groups are determined among limit groups by their profinite completions. As a corollary, the set of surface words in a free group is closed in the profinite topology.

We describe the infinite dihedral group as automaton group. We collect basic results and give full proofs in details for all statements.

We describe a bound on the degree of the generators for some adjoint rings on surfaces and threefolds.

Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…

In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.