\(K\)-loops and Bruck loops on \(\mathbb{R}\times\mathbb{R}\) (Q686658)
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scientific article; zbMATH DE number 428598
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(K\)-loops and Bruck loops on \(\mathbb{R}\times\mathbb{R}\) |
scientific article; zbMATH DE number 428598 |
Statements
\(K\)-loops and Bruck loops on \(\mathbb{R}\times\mathbb{R}\) (English)
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13 October 1993
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\(K\)-loops are certain generalizations of neardomains. Using the function \(\lambda(x) = \cosh x\), \(K\)-loops on \(\mathbb{R}\times \mathbb{R}\) are constructed. Since every \(K\)-loop is a Bruck loop, we also have examples for Bruck loops. Furthermore the group of automorphisms \(\delta_{a,b}\) of the \(K\)-loop which satisfy the equation \(a+(b+c) = (a,b)+\delta_{a,b}(c)\) is examined.
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generalizations of neardomains
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\(K\)-loops
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Bruck loops
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group of automorphisms
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