Related papers: On L.G. Kov\`acs' problem

Given an extension $0\to V\to G\to Q\to1$ of locally compact groups, with $V$ abelian, and a compatible essentially bijective $1$-cocycle $\eta\colon Q\to\hat V$, we define a dual unitary $2$-cocycle on $G$ and show that the associated…

We consider groups of the form $G=AB$ with two locally cyclic subgroups $A$ and $B$. The structure of these groups is determined in the cases when $A$ and $B$ are both periodic or when one of them is periodic and the other is not. Together…

The path spaces of a directed graph play an important role in the study of graph $\css$. These are topological spaces that were originally constructed using groupoid and inverse semigroup techniques. In this paper, we develop a simple,…

A finite group $G$ is a called a DCI-group if any two isomorphic Cayley digraphs of $G$ are also isomorphic via an automorphism of $G$. If $G$ is a non-abelian generalised dihedral DCI-group, then Dobson, Muzychuk, and Spiga proved that $G$…

Let $G=D_p$ be the dihedral group of order $2p$, where $p$ is an odd prime. Let $k$ an algebraically closed field of characteristic $p$. We show that any action of $G$ on the ring $k[[y]]$ can be lifted to an action on $R[[y]]$, where $R$…

Given any digraph $D$ without loops or multiple arcs, there is a natural construction of a semigroup $\langle D\rangle$ of transformations. To every arc $(a,b)$ of $D$ is associated the idempotent transformation $(a\to b)$ mapping $a$ to…

We show that Dranishnikov's asymptotic property C is preserved by direct products and the free product of discrete metric spaces. In particular, if $G$ and $H$ are groups with asymptotic property C, then both $G \times H$ and $G * H$ have…

Let $G,D_{0},D_{1}$ be finite groups such that $D_{0}\trianglelefteq D_{1}$ are groups of automorphisms of $G$ that contain the inner automorphisms of $G$. Assume that $D_{1}/D_{0}$ has a normal $2$-complement and that $D_{1}$ acts…

We show that the semidirect product of a group $C$ by $A*_D B$ is isomorphic to the free product of $A\rtimes C$ and $B\rtimes C$ amalgamated at $D\rtimes C$, where $A$, $B$ and $C$ are arbitrary groups. Moreover, we apply this theorem to…

Let for a prime $p$, $\mathfrak{X}$ (respectively $\mathfrak{Y}$) be the class of all $p$-biprimitively finite (respectively periodic $p$-conjugatively biprimitively finite) groups and $G\in \mathfrak{X}$ (respectively $G\in \mathfrak{Y}$),…

We consider the hidden subgroup problem on the semi-direct product of cyclic groups $\Z_{N}\rtimes\Z_{p}$ with some restriction on $N$ and $p$. By using the homomorphic properties, we present a class of semi-direct product groups in which…

Let $X=GD$ be a group, where $G$ is a nonabelian simple group and $D$ is a dihedral group. These groups $X$ are closely related to regular Cayley maps. The main theorems of this paper describes $X$.

Let $V$ be a finite-dimensional vector space over the field with $p$ elements, where $p$ is a prime number. Given arbitrary $\alpha,\beta\in \mathrm{GL}(V)$, we consider the semidirect products $V\rtimes\langle \alpha\rangle$ and…

Nonuniqueness of semidirect decompositions of groups is an insufficiently studied question in contrast to direct decompositions. We obtain some results about semidirect decompositions for semidirect products with factors which are…

Let k be an algebraically closed field of characteristic p>>0. Let $X\rightarrow Y$ be a symplectic resolution. There are two questions which motivates this work. One question is a construction of an action of a group on the category…

In this manuscript, a solution to Problem 18.91(b) in the Kourovka Notebook is given by proving the following theorem. Let $P$ be a Sylow $p$-subgroup of a group $G$ with $|P| = p^n$. Suppose that there is an integer $k$ such that $1 < k <…

In this note we study the dynamics of the natural evaluation action of the group of isometries $G$ of a locally compact metric space $(X,d)$ with one end. Using the notion of pseudo-components introduced by S. Gao and A. S. Kechris we show…

Let B be a commutative $\mathbb{Z}$-graded domain of characteristic zero. An element f of B is said to be cylindrical if it is nonzero, homogeneous of nonzero degree, and such that $B_{(f)}$ is a polynomial ring in one variable over a…

A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…

In the present work we consider differential rings of the form $(\mathcal B,D)$ where $\mathcal B$ is a Danielewski surface and $D$ is a locally nilpotent derivation on $\mathcal B$. Influenced by several recent works, we describe the…