相关论文: On The Isomorphism Classes Of Transversals III

We investigate two Galois connection between the congruence lattice and the lattice of subgroups of the displacement group of left quasigroups. Such connections were already studied for racks and quandles. We introduce the class of left…

Let G denote a group and let W be an algebra over a commutative ring R. We will say that W is a G-graded twisted algebra (not necessarily commutative, neither associative) if there exists a G-grading W=\bigoplus_{g \in G}W_{g} where each…

We give a general construction for right conjugacy closed loops, using $GL(2,q)$ for $q$ a prime power. Under certain conditions, the loops constructed are simple, giving the first general construction for finite, simple right conjugacy…

If H is a flat group of automorphisms of finite rank n of a totally disconnected, locally compact group G, then each orbit of H in the metric space B(G) of compact, open subgroups of G is quasi-isometric to n-dimensional euclidean space. In…

Let $G=\left\langle S|R_{A}\right\rangle $ be a semigroup with generating set $ S$ and equivalences $R_{A}$ among $S$ determined by a matrix $A$. This paper investigates the complexity of $G$-shift spaces by yielding the topological…

We classify $\mathcal{R}$- and $\mathcal{L}$-cross-sections of wreath products of finite inverse symmetric semigroups $\mathcal{IS}_m \wr_p \mathcal{IS}_n$ up to isomorphism. We show that every isomorphism of $\mathcal{R}$ ($\mathcal{L}$-)…

We give a classification of all quasitriangular structures and ribbon elements of $\mathcal{D}(G)$ explicitly in terms of group homomorphisms and central subgroups. This can equivalently be interpreted as an explicit description of all…

A class of one-relator groups such that every group in the class is determined by a triple of integers and is an HNN-extension of some Baumslag -- Solitar group is considered. A criterion for two groups in this class to be isomorphic and…

Let G be a closed subgroup of the isometry group of a proper CAT(0)-space X. We show that if G is non-elementary and contains a rank-one element then its second bounded cohomology group with coefficients in the regular representation is…

In this paper, we develop a cohomology theory of a left-symmetric conformal algebra and study its some applications. We define the cohomology of a left-symmetric conformal algebra, and then give an isomorphism between the cohomology spaces…

We compute the chains associated to the left-invariant CR structures on the three-sphere. These structures are characterized by a single real modulus $a$. For the standard structure $a=1$, the chains are well-known and are closed curves. We…

Two groups are virtually isomorphic if they can be obtained one from the other via a finite number of steps, where each step consists in taking a finite extension or a finite index subgroup (or viceversa). Virtually isomorphic groups are…

We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids. We compare the holomorph with the monoid of mappings that preserve the ternary heap…

Biinvariant diagonal classes give rise to right inverses of the Kirwan map. By means of multivalued perturbations of the gradient flow equation such classes are constructed explicitly for $S^1$-Hamiltonian spaces. Moreover, the notion of…

Let $\mathbf{G}=\{G_1,\dots,G_{s}\}$ be a collection of $s$ bipartite graphs with the same bipartition $V=(X,Y)$. For a path $P$ with $V(P)=V$ and $|E(P)|=s$, if there exists an injection $\phi$: $E(P)\rightarrow [s]$ such that $e\in…

We prove that if the multiplication group $Mult(L)$ of a connected $2$-dimensional topological loop is a Lie group, then $Mult(L)$ is an elementary filiform nilpotent Lie group of dimension at least $4$. Moreover, we describe loops having…

We prove that if $G$ is finite 2-generated $p$-group of nilpotence class at most 2 then the group algebra of $G$ with coefficients in the field with $p$ elements determines $G$ up to isomorphisms.

A left invariant Z-Randers metric on the five-dimensional Heisenberg group is a left invariant Randers metric with deformation vector from the center of the Heisenberg algebra. In this note we prove that for every left invariant Z-Randers…

A Lie group G is called a trace class group if for every irreducible unitary representation R of G and every C-infinity function f with compact support the operator R(f) is of trace class. In this note we prove that the semidirect product…

Let $G$ be a right-angled Artin group with $|\mathrm{Out}(G)|<+\infty$. We prove that if a countable group $H$ with bounded torsion is measure equivalent to $G$, with an $L^1$-integrable measure equivalence cocycle towards $G$, then $H$ is…