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dc.contributor.author |
Banakh, T. |
|
dc.contributor.author |
Gavrylkiv, V. |
|
dc.date.accessioned |
2019-06-14T03:34:04Z |
|
dc.date.available |
2019-06-14T03:34:04Z |
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dc.date.issued |
2008 |
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dc.identifier.citation |
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. |
uk_UA |
dc.identifier.issn |
1726-3255 |
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dc.identifier.other |
2000 Mathematics Subject Classification: 20M99, 54B20. |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/153356 |
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dc.description.abstract |
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. |
uk_UA |
dc.language.iso |
en |
uk_UA |
dc.publisher |
Інститут прикладної математики і механіки НАН України |
uk_UA |
dc.relation.ispartof |
Algebra and Discrete Mathematics |
|
dc.title |
Algebra in superextensions of groups, II: cancelativity and centers |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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