Related papers: Some Remarks on Groups with Action on Itself

The author proposes a method for investigating actions of finite groups on aspherical spaces. Complete homotopy classification of free actions of finite groups on aspherical spaces is obtained. Also there are some results about non-free…

We introduce the property of having good subgroups for actions of countable discrete groups on compact metrizable spaces, and show that it implies comparison when the acting group is amenable. As a consequence, free actions on…

In this paper we consider all orientation-preserving $\mathbb{Z}_{4}$-actions on $3$-dimensional handlebodies $V_g$ of genus $g>0$. We study the graph of groups $(\Gamma($v$),\mathbf{G(v)})$, which determines a handlebody orbifold…

A global action is an algebraic analogue of a topological space. It consists of group actions $G_\alpha\curvearrowright X_\alpha$, $(\alpha\in\Phi)$, which fulfill a certain compatibility condition. We investigate the homotopy theory of…

We study locally compact convergence groups, in particular the link between the convergence property and the Specker compactifications (a genaralization of the ends) of a group.

The aim of this article is to explore global and local properties of finite groups whose integral group rings have only trivial central units, so-called cut groups. For such a group we study actions of Galois groups on its character table…

The action dimension of a discrete group G, actdim(G), is defined to be the smallest integer m such that G admits a properly discontinuous action on a contractible m-manifold. If no such m exists, we define actdim(G) = infty. Bestvina,…

We consider large finite group-actions on surfaces and discuss and compare various notions for such actions: Hurwitz actions and Hurwitz groups; maximal reducible and completely reducible actions; bounding and geometrically bounding…

We study actions of discrete groups on contractible topological spaces in which either (1) all stabilizers lie in the family of subgroups of prime power order or (2) all stabilizers lie in the family of finite subgroups. We compare the…

We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative…

We investigate the geometry of median metric spaces. The group-theoretic applications are towards Kazhdan's property (T) and Haagerup's property.

We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi-Brauer surfaces over fields of characteristic zero.

For a group acting on a hyperbolic space, we set up an algorithm in the group algebra showing that ideals generated by few elements are free, where few is a function of the minimal displacement of the action, and derive algebraic,…

Let $\Gamma$ be a finitely generated group which admits an action by homeomorphisms on a compact metrizable space $X$. We show that there is a metric on $X$ defining the original topology such that for this metric, the action is by…

We discuss properties of orbits of (semi)group actions on locally compact groups G. In particular, we show that if a compactly generated locally compact abelian group acts distally on G then the closure of each of its orbits is a minimal…

In this notes we give details of the proofs performed with GAP of the theorems of our paper "Pointed Hopf Algebras over the Sporadic Simple Groups".

We describe an algorithm that constructs a list of all topological types of holomorphic actions of a finite group on a compact Riemann surface $C$ of genus at least $g \geq 2$ with $C/G \cong \mathbb{P}^1$.

In this paper we consider all orientation-preserving $\mathbb{Z}_{p^2}$-actions on 3-dimensional handlebodies $V_g$ of genus $g>0$ for $p$ an odd prime. To do so, we examine particular graphs of groups $(\Gamma($v$),\mathbf{G(v)})$ in…

We establish a connection between two well-studied spaces of countable groups: the space of group operations and the space of marked groups. This connection shows that the two spaces are equivalent in terms of generic properties in the…

We introduce the definition of totally nonfree actions of groups; such actions are naturally related to the theory of characters of groups and their factor-representations of type II. This short note is a brief exposition of a part of a…