Algebra and Discrete Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra Discrete Math.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra and Discrete Mathematics, 2008, Issue 4, Pages 1–14 (Mi adm174)  

This article is cited in 8 scientific papers (total in 8 papers)

RESEARCH ARTICLE

Algebra in superextensions of groups, II: cancelativity and centers

Taras Banakha, Volodymyr Gavrylkivb

a Ivan Franko National University of Lviv, Universytetska 1, 79000, Ukraine
b Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
Full-text PDF (243 kB) Citations (8)
Abstract: Given a countable group $X$ we study the algebraic structure of its superextension $\lambda(X)$. This is a right-topological semigroup consisting of all maximal linked systems on $X$ endowed with the operation
$$ \mathcal A\circ\mathcal B=\{C\subset X:\{x\in X:x^{-1}C\in\mathcal B\}\in\mathcal A\} $$
that extends the group operation of $X$. We show that the subsemigroup $\lambda^\circ(X)$ of free maximal linked systems contains an open dense subset of right cancelable elements. Also we prove that the topological center of $\lambda(X)$ coincides with the subsemigroup $\lambda^\bullet(X)$ of all maximal linked systems with finite support. This result is applied to show that the algebraic center of $\lambda(X)$ coincides with the algebraic center of $X$ provide $X$ is countably infinite. On the other hand, for finite groups $X$ of order $3\le|X|\le5$ the algebraic center of $\lambda(X)$ is strictly larger than the algebraic center of $X$.
Keywords: Superextension, right-topological semigroup, cancelable element, topological center, algebraic center.
Received: 14.02.2008
Revised: 25.08.2008
Bibliographic databases:
Document Type: Article
MSC: 20M99, 54B20
Language: English
Citation: Taras Banakh, Volodymyr Gavrylkiv, “Algebra in superextensions of groups, II: cancelativity and centers”, Algebra Discrete Math., 2008, no. 4, 1–14
Citation in format AMSBIB
\Bibitem{BanGav08}
\by Taras~Banakh, Volodymyr~Gavrylkiv
\paper Algebra in superextensions of groups, II: cancelativity and centers
\jour Algebra Discrete Math.
\yr 2008
\issue 4
\pages 1--14
\mathnet{http://mi.mathnet.ru/adm174}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2541173}
\zmath{https://zbmath.org/?q=an:1199.22006}
Linking options:
  • https://www.mathnet.ru/eng/adm174
  • https://www.mathnet.ru/eng/adm/y2008/i4/p1
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Algebra and Discrete Mathematics
    Statistics & downloads:
    Abstract page:117
    Full-text PDF :72
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024