Algebra in superextensions of groups, II: cancelativity and centers
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Algebra in superextensions of groups, II: cancelativity and centers
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| Creator |
Banakh, T.
Gavrylkiv, V. |
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| 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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| Date |
2019-06-14T03:34:04Z
2019-06-14T03:34:04Z 2008 |
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| Type |
Article
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| Identifier |
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. http://dspace.nbuv.gov.ua/handle/123456789/153356 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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