Abstract
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.
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Drápal, A., Vojtěchovský, P. A variety of Steiner loops satisfying Moufang’s theorem: a solution to Rajah’s Problem. Aequat. Math. 94, 97–101 (2020). https://doi.org/10.1007/s00010-019-00692-3
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DOI: https://doi.org/10.1007/s00010-019-00692-3