On the cardinality of \(2\)-bases in quasigroups (Q1337804)
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scientific article; zbMATH DE number 687068
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the cardinality of \(2\)-bases in quasigroups |
scientific article; zbMATH DE number 687068 |
Statements
On the cardinality of \(2\)-bases in quasigroups (English)
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13 November 1994
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Eine Teilmenge \(B\) einer Quasigruppe \((Q,*)\), für die \(B*B := \{b * b' \mid b,b' \in B\} = Q\) gilt, ist eine ``2-Basis'' von \(Q\). Ist \(n\) die Mächtigkeit von \(Q\), so wird für die minimale Mächtigkeit \(k(Q)\) einer 2-Basis von \(Q\) die asymptotische Abschätzung nach oben: \(k(Q) = o(n^{(1/2) + \varepsilon})\); \(\varepsilon > 0\), \(| Q | = n\) bewiesen.
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minimal cardinality
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2-bases
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quasigroups
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asymptotic estimates
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0.7270774841308594
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0.7269472479820251
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