| Autor: |
Drápal, Aleš, Vojtěchovský, Petr |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Aequationes mathematicae, volume 94 (2020), pages 97-101 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s00010-019-00692-3 |
| Popis: |
A loop $X$ is said to satisfy Moufang's theorem if for every $x,y,z\in X$ such that $x(yz)=(xy)z$ the subloop generated by $x$, $y$, $z$ is a group. We prove that the variety $V$ of Steiner loops satisfying the identity $(xz)(((xy)z)(yz)) = ((xz)((xy)z))(yz)$ is not contained in the variety of Moufang loops, yet every loop in $V$ satisfies Moufang's theorem. This solves a problem posed by Andrew Rajah. |
| Databáze: |
arXiv |
| Externí odkaz: |
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