Related papers: Space functions of groups
We will explore the nature of when certain finite groups have an equal covering, and when finite groups do not. Not to be confused with the concept of a cover group, a covering of a group is a collection of proper subgroups whose…
In this paper we study the idea of strong-I^K-convergence of functions which is common generalization of strong-I*-convergence of functions in probabilistic metric spaces. We also study strong-I^K-limit points of functions in the same…
We consider several subgroup-related algorithmic questions in groups, modeled after the classic computational lattice problems, and study their computational complexity. We find polynomial time solutions to problems like finding a subgroup…
In this paper we study a subclass of subcartesian space-the orbit space of a proper action of Lie group on smooth manifold. We show that continuous functions on orbit space can be approximated by smooth functions.
We establish sharp upper bounds for the topological complexity of motion planning problem in spaces with small fundamental group, i.e. when it is finite of small order or has small cohomological dimension.
We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…
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 study constructions of groups, in particular of groups of intermediate rank, which are accessible to surgery techniques.
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
In this survey article, we summarize some recent progress and problems on the symplectomorphism groups, with an emphasis on the connection to the space of ball-packings.
We investigate the geometry of median metric spaces. The group-theoretic applications are towards Kazhdan's property (T) and Haagerup's property.
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
We analyze the Gottlieb groups of function spaces. Our results lead to explicit decompositions of the Gottlieb groups of many function spaces map(X,Y)---including the (iterated) free loop space of Y---directly in terms of the Gottlieb…
We calculate zeta and normal zeta functions of space groups with the point group isomorphic to the cyclic group of order 2. The obtained results are applied to determine the number of subgroups, resp. normal subgroups, of a given index for…
We survey the known results regarding the boundaries of word-hyperbolic groups.
We compute the topological complexity of Eilenberg-Mac Lane spaces associated to the group of automorphisms of a finitely generated free group which act by conjugation on a given basis, and to certain subgroups.
We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of…
We explain why numbers occurring in the classification of polygon spaces coincide with numbers of self-dual equivalence classes of threshold functions, or of regular Boolean functions, or of decisive weighted majority games.
We construct the meromorphic functions invariant under the action of the sense-preserving wallpaper groups on the complex plane. We discuss possible generalisa-tions of this to the general wallpaper groups. This provides the answer to a…
We study the complexity of computation in finitely generated free left, right and two-sided adequate semigroups and monoids. We present polynomial time (quadratic in the RAM model of computation) algorithms to solve the word problem and…