Algebra in superextensions of groups, II: cancelativity and centers
Given a countable group X we study the algebraic structure of its
 superextension λ(X). This is a right-topological semigroup consisting of all maximal linked systems on X endowed with the operation 
 
 A∘B={C⊂X:{x∈X:x−1C∈B}∈A} 
 
 that extends the grou...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2008 |
| ISSN: | 1726-3255 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/153356 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Algebra in superextensions of groups, II: cancelativity and centers / T. Banakh, V. Gavrylkiv // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 4. — С. 1–14. — Бібліогр.: 10 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862737067271782400 |
|---|---|
| author | Banakh, T. Gavrylkiv, V. |
| author_facet | Banakh, T. Gavrylkiv, V. |
| citation_txt | Algebra in superextensions of groups, II: cancelativity and centers / T. Banakh, V. Gavrylkiv // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 4. — С. 1–14. — Бібліогр.: 10 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Given a countable group X we study the algebraic structure of its
superextension λ(X). This is a right-topological semigroup consisting of all maximal linked systems on X endowed with the operation 

A∘B={C⊂X:{x∈X:x−1C∈B}∈A} 

that extends the group operation of X. We show that the subsemigroup λ∘(X) of free maximal linked systems contains an open dense subset of right cancelable elements. Also we prove that the topological center of λ(X) coincides with the subsemigroup λ∙(X) of all maximal linked systems with finite support. This result is applied to show that the algebraic center of λ(X) coincides with the algebraic center of X provided X is countably infinite. On the other hand, for finite groups X of order 3≤|X|≤5 the algebraic center of λ(X) is strictly larger than the algebraic center of X.
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| first_indexed | 2025-12-07T19:57:24Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-153356 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:57:24Z |
| publishDate | 2008 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Banakh, T. Gavrylkiv, V. 2019-06-14T03:34:04Z 2019-06-14T03:34:04Z 2008 Algebra in superextensions of groups, II: cancelativity and centers / T. Banakh, V. Gavrylkiv // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 4. — С. 1–14. — Бібліогр.: 10 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 20M99, 54B20. https://nasplib.isofts.kiev.ua/handle/123456789/153356 Given a countable group X we study the algebraic structure of its
 superextension λ(X). This is a right-topological semigroup consisting of all maximal linked systems on X endowed with the operation 
 
 A∘B={C⊂X:{x∈X:x−1C∈B}∈A} 
 
 that extends the group operation of X. We show that the subsemigroup λ∘(X) of free maximal linked systems contains an open dense subset of right cancelable elements. Also we prove that the topological center of λ(X) coincides with the subsemigroup λ∙(X) of all maximal linked systems with finite support. This result is applied to show that the algebraic center of λ(X) coincides with the algebraic center of X provided X is countably infinite. On the other hand, for finite groups X of order 3≤|X|≤5 the algebraic center of λ(X) is strictly larger than the algebraic center of X. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Algebra in superextensions of groups, II: cancelativity and centers Article published earlier |
| spellingShingle | Algebra in superextensions of groups, II: cancelativity and centers Banakh, T. Gavrylkiv, V. |
| title | Algebra in superextensions of groups, II: cancelativity and centers |
| title_full | Algebra in superextensions of groups, II: cancelativity and centers |
| title_fullStr | Algebra in superextensions of groups, II: cancelativity and centers |
| title_full_unstemmed | Algebra in superextensions of groups, II: cancelativity and centers |
| title_short | Algebra in superextensions of groups, II: cancelativity and centers |
| title_sort | algebra in superextensions of groups, ii: cancelativity and centers |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/153356 |
| work_keys_str_mv | AT banakht algebrainsuperextensionsofgroupsiicancelativityandcenters AT gavrylkivv algebrainsuperextensionsofgroupsiicancelativityandcenters |