Multiplication groups of finite loops that fix at most two points (Q1840612)
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scientific article; zbMATH DE number 1563177
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multiplication groups of finite loops that fix at most two points |
scientific article; zbMATH DE number 1563177 |
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Multiplication groups of finite loops that fix at most two points (English)
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22 July 2001
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Let \(Q\) be a finite loop (quasigroup with identity), \(L_a(x):=ax\), \(R_a(x):=xa\). A proof is offered that \(Q\) has to be an Abelian group if every permutation of its multiplication group \(\{L_a,R_a\mid a\in Q\}\) has at most two fixed points. An extension to the infinite case is alluded to in the introduction.
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finite loops
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multiplication groups
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permutations
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fixed points
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Abelian groups
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infinite loops
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