Abstract
A loop which satisfies the identitiesx 2 =e, xe = ex = x, andx(yx) = (xy) x = y is called a generalized Steiner loop. In this paper it is shown that a generalized Steiner loop is a groupoid with a single lawx(((yy) z) x) = z.
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Reference
Mendelsohn, N. S.,A Natural Generalization of Steiner Triple Systems, to appear in the Proceedings of the Second Atlas Symposium held in Oxford, England, Aug. 1969. (Preprints are available.)
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Mendelsohn, N.S. A single groupoid identity for Steiner loops. Aequat. Math. 6, 228–230 (1971). https://doi.org/10.1007/BF01819755
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DOI: https://doi.org/10.1007/BF01819755