scholarly journals Searching Big Data via cyclic groups

2017 ◽  
Vol 6 (2) ◽  
pp. 47-53
Author(s):  
Timur Karacay
Keyword(s):  
Big Data ◽  
Group Structure ◽  
Linear Search ◽  
Topological Groups ◽  
Cyclic Subgroups ◽  
Cyclic Groups ◽  
Dual Groups

We look up for a certain information in big data. To achieve this task we first endow the big data with a group structure and partition it to it’s cyclic subgroups. We devise a method to search the whole big data starting from the smallest subroup through the largest one. Our method eventually exhausts the whole big data. Keywords: BigData, topological groups, dual groups, linear search.

scholarly journals More on generalized topological groups

2013 ◽  
Vol 22 (1) ◽  
pp. 47-51
Author(s):  
MURAD HUSSAIN ◽  
◽  
MOIZ UD DIN KHAN ◽  
CENAP OZEL ◽  
◽  
...  
Keyword(s):  
Topological Group ◽  
Group Structure ◽  
Topological Groups

In the paper [Hussain, M., Khan, M. and Ozel, C., ¨ On Generalized Topological Groups] we defined the generalized topological group structure and we proved some basic results. In this work we introduce the notions of ultra Hausdorffness and ultra G-Hausdorffness and we give the relation between the ultra G-Hausdorffness and G-compactness.

Sur les Sous-Groupes Purifiables des Groupes Abéliens Primaires

1990 ◽  
Vol 33 (1) ◽  
pp. 11-17 ◽  
Author(s):  
K. Benabdallah ◽  
C. Piché
Keyword(s):  
Abelian Groups ◽  
Divisible Group ◽  
Direct Sums ◽  
Cyclic Subgroups ◽  
Cyclic Groups ◽  
Direct Sum

AbstractThe class of primary abelian groups whose subsocles are purifiable is not yet completely characterized and it contains the class of direct sums of cyclic groups and torsion complete groups. In sharp constrast with this, the class of groups whose p2-bounded subgroups are purifiable consist only of those groups which are the direct sum of a bounded and a divisible group. Various tools are developed and a short application to the pure envelopes of cyclic subgroups is given in the last section.

scholarly journals A study of some aspects of topological groups

Filomat ◽  
2007 ◽  
Vol 21 (1) ◽  
pp. 55-65
Author(s):  
M.R. Adhikari ◽  
M. Rahaman
Keyword(s):  
Topological Group ◽  
Group Structure ◽  
Base Point ◽  
Homotopy Category ◽  
Topological Spaces ◽  
Topological Groups ◽  
Homotopy Classes ◽  
Continuous Maps

The aim of this paper is to find a generalization of topological groups. The concept arises out of the investigation to obtain a group structure on the set [X,Y], of homotopy classes of maps from a space X to a given space Y for all X which is natural with respect to X. We also study the generalized topological groups. Finally, associated with each generalized topological group we construct a contra variant functor from the homotopy category of pointed topological spaces and base point preserving continuous maps to the category of groups and homomorphism.

scholarly journals Big Data Process Engineering under Manifold Coordinate Systems

2021 ◽  
Vol 18 ◽  
pp. 7-11
Author(s):  
Volodymyr Riznyk
Keyword(s):  
Big Data ◽  
High Performance ◽  
Scientific Basis ◽  
Process Engineering ◽  
Optimal Placement ◽  
Coordinate Systems ◽  
Cyclic Groups ◽  
Data Coding ◽  
Data Process ◽  
General Number

This paper involves techniques for improving the quality indices of big data process engineering with respect to high-performance coded design, transmission speed, and reliability under manifold coordinate systems. The system formed with limited number of basis vectors. The set of modular sums of the vectors including themselves form t-dimensional toroidal coordinate grid over the toroid, and the basis is sub-set of general number of grid coordinate set. These design techniques make it possible to configure high performance information technology for big data coding design and vector signal processing. The underlying mathematical principles relate to the optimal placement of structural elements in spatially or temporally distributed systems by the appropriate algebraic constructions based on cyclic groups in extensions of Galois fields, and development of the scientific basis for optimal solutions for wide classes of technological problems in big data process engineering and computer science.

scholarly journals On the Exponent of the NK0-Groups of Virtually Infinite Cyclic Groups

2002 ◽  
Vol 45 (2) ◽  
pp. 180-195 ◽  
Author(s):  
Francis X. Connolly ◽  
Stratos Prassidis
Keyword(s):  
Large Class ◽  
The Other ◽  
Main Difficulty ◽  
Cyclic Subgroups ◽  
Cyclic Groups ◽  
Other Hand

AbstractIt is known that the K-theory of a large class of groups can be computed from the K-theory of their virtually infinite cyclic subgroups. On the other hand, Nil-groups appear to be the obstacle in calculations involving the K-theory of the latter. The main difficulty in the calculation of Nil-groups is that they are infinitely generated when they do not vanish. We develop methods for computing the exponent of NK0-groups that appear in the calculation of the K0-groups of virtually infinite cyclic groups.

scholarly journals Subgroups of direct products closely approximated by direct sums

2017 ◽  
Vol 29 (5) ◽  
pp. 1125-1144 ◽  
Author(s):  
Maria Ferrer ◽  
Salvador Hernández ◽  
Dmitri Shakhmatov
Keyword(s):  
Direct Product ◽  
Coding Theory ◽  
List Type ◽  
Direct Products ◽  
Topological Groups ◽  
Product Topology ◽  
Direct Sums ◽  
Cyclic Groups ◽  
Finite Set ◽  
Infinite Set

AbstractLet I be an infinite set, let {\{G_{i}:i\in I\}} be a family of (topological) groups and let {G=\prod_{i\in I}G_{i}} be its direct product. For {J\subseteq I}, {p_{J}:G\to\prod_{j\in J}G_{j}} denotes the projection. We say that a subgroup H of G is(i)uniformly controllable in G provided that for every finite set {J\subseteq I} there exists a finite set {K\subseteq I} such that {p_{J}(H)=p_{J}(H\cap\bigoplus_{i\in K}G_{i})}, (ii)controllable in G provided that {p_{J}(H)=p_{J}(H\cap\bigoplus_{i\in I}G_{i})} for every finite set {J\subseteq I},(iii)weakly controllable in G if {H\cap\bigoplus_{i\in I}G_{i}} is dense in H, when G is equipped with the Tychonoff product topology.One easily proves that (i) {\Rightarrow} (ii) {\Rightarrow} (iii). We thoroughly investigate the question as to when these two arrows can be reversed. We prove that the first arrow can be reversed when H is compact, but the second arrow cannot be reversed even when H is compact. Both arrows can be reversed if all groups {G_{i}} are finite. When {G_{i}=A} for all {i\in I}, where A is an abelian group, we show that the first arrow can be reversed for all subgroups H of G if and only if A is finitely generated. We also describe compact groups topologically isomorphic to a direct product of countably many cyclic groups. Connections with coding theory are highlighted.

scholarly journals On orderability of topological groups

1985 ◽  
Vol 8 (4) ◽  
pp. 747-754
Author(s):  
G. Rangan
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Group Structure ◽  
Locally Compact Abelian Group ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Topological Groups ◽  
Locally Compact ◽  
Necessary And Sufficient ◽  
Totally Disconnected

A necessary and sufficient condition for a topological group whose topology can be induced by a total order compatible with the group structure is given and such groups are called ordered or orderable topological groups. A separable totally disconnected ordered topological group is proved to be non-archimedean metrizable while the converse is shown to be false by means of an example. A necessary and sufficient condition for a no-totally disconnected locally compact abelian group to be orderable is also given.

scholarly journals Classifying Spaces for the Family of Virtually Cyclic Subgroups of Braid Groups

2018 ◽  
Vol 2020 (5) ◽  
pp. 1575-1600
Author(s):  
Ramón Flores ◽  
Juan González-Meneses
Keyword(s):  
Braid Group ◽  
Braid Groups ◽  
Classifying Spaces ◽  
Classifying Space ◽  
Cyclic Subgroups ◽  
Cyclic Groups ◽  
Pure Braid Group ◽  
Minimal Dimension ◽  
The Family

Abstract We prove that, for n ≥ 3, the minimal dimension of a model of the classifying space of the braid group $B_{n}$, and of the pure braid group $P_{n}$, with respect to the family of virtually cyclic groups is n.

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