Algebra in superextensions of groups, I: zeros and commutativity
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Algebra in superextensions of groups, I: zeros and commutativity
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| Creator |
Banakh, T.T.
Gavrylkiv, V. Nykyforchyn, O. |
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| Description |
Given a 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 characterize right zeros of λ(X) as invariant maximal linked systems on X and prove that λ(X) has a right zero if and only if each element of X has odd order. On the other hand, the semigroup λ(X) contains a left zero if and only if it contains a zero if and only if X has odd order |X|≤5. The semigroup λ(X) is commutative if and only if |X|≤4. We finish the paper with a complete description of the algebraic structure of the semigroups λ(X) for all groups X of cardinality |X|≤5. |
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| Date |
2019-06-14T03:39:46Z
2019-06-14T03:39:46Z 2008 |
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| Type |
Article
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| Identifier |
Algebra in superextensions of groups, I: zeros and commutativity / T.T. Banakh, V. Gavrylkiv, O. Nykyforchyn // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 3. — С. 1–29. — Бібліогр.: 13 назв. — англ.
1726-3255 2000 Mathematics Subject Classification: 20M99, 54B20. http://dspace.nbuv.gov.ua/handle/123456789/153373 |
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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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