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 group operation of X. We show that the subse...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2008
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| Zitieren: | 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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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Algebra in superextensions of groups, II: cancelativity and centers |
| spellingShingle |
Algebra in superextensions of groups, II: cancelativity and centers Banakh, T. Gavrylkiv, V. |
| title_short |
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_sort |
algebra in superextensions of groups, ii: cancelativity and centers |
| author |
Banakh, T. Gavrylkiv, V. |
| author_facet |
Banakh, T. Gavrylkiv, V. |
| publishDate |
2008 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/153356 |
| 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. |
| work_keys_str_mv |
AT banakht algebrainsuperextensionsofgroupsiicancelativityandcenters AT gavrylkivv algebrainsuperextensionsofgroupsiicancelativityandcenters |
| first_indexed |
2025-12-07T19:57:24Z |
| last_indexed |
2025-12-07T19:57:24Z |
| _version_ |
1850880761167609856 |