Related papers: Egyptian fractions on groups
We develop a formula for tautological integrals over geometric subsets of the Hilbert scheme of points on complex manifolds. As an illustration of the theory, we derive a new iterated residue formula for the number of nodal curves in…
Topological algebras have properties that extend naturally to those of topological groups [8, 9], but is it the case that semi-direct products exist as in the category of groups? Firstly, we express concepts in categorical language that…
We develop a method that we call \emph{omission of intervals}, for establishing topological properties of subsets of the real line based on their combinatorial structure. Using this method, we obtain conceptual proofs of the fundamental…
We investigate some properties of topological groups related to disconnectedness or Archimedeanness. We prove or disprove the preservation of those under operations as subgroups, quotients, products, etc. Characterizations of…
This article is devoted to sets having the Moran structure. The main attention is given to topological, metric, and fractal properties of certain sets whose elements have restrictions on using digits or combinations of digits in own…
The additivity with respect to exact sequences is notoriously a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by deeply exploiting their structure. On the other hand, a solvable…
A brief survey of some aspects of noetherian Hopf algebras is given, concentrating on structure, homology, and classification, and accompanied by a panoply of open problems.
It is shown that every separable abelian topological group is isomorphic with a topological subgroup of a monothetic group (that is, a topological group with a single topological generator). In particular, every separable metrizable abelian…
This is a survey on old and new results as well as an introduction to various related basic notions and concepts, based on two talks given at the International Workshop on Geometry and Analysis in Kemerovo (Sobolev Institute of Mathematics,…
Structural properties of unitary groups over local, not necessarily commutative, rings are developed, with applications to the computation of the orders of these groups (when finite) and to the degrees of the irreducible constituents of the…
Motivated by Quantum Mechanics considerations, we expose some cross product constructions on a groupoid structure. Furthermore, critical remarks are made on some basic formal aspects of the Hopf algebra structure.
In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…
We give a general construction of topological groups from combinatorial structures such as trees, towers, gaps, and subadditive functions. We connect topological properties of corresponding groups with combinatorial properties of these…
The rational homology group of the order complex of non-even partitions of a finite set is calculated. A twisted version of the Goresky-MacPherson approach to similar homology calculations is proposed.
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
We consider metric ultraproducts of finite groups with respect to some classes of length functions. All sofic groups embed into these ultraproducts. We study embeddings of normed groups. We also show that in some natural situations such an…
The results of the paper concern the topological structure of complete riemannian manifolds with cyclic holonomy groups and low-dimensional orientable complete flat manifolds. We also discuss related results such as the affine…
We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.
We consider abelain subgroups of small index in finite groups. More generally, we consider subgroups such that the product of their index by the index of their centralizer is small.