Geodesic
A class of quasigroups solving a problem of ergodic theory
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 2, pp. 409-414

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A pointed quasigroup is said to be semicentral if it is principally isotopic to a group via a permutation on one side and a group automorphism on the other. Convex combinations of permutation matrices given by the one-sided multiplications in a semicentral quasigroup then yield doubly stochastic transition matrices of finite Markov chains in which the entropic behaviour at any time is independent of the initial state.
Classification : 20N05, 60J10
Keywords: quasigroup; Latin square; Markov chain; doubly stochastic matrix; ergodic; superergodic; dripping faucet; group isotope; central quasigroup; semicentral quasigroup; $T$-quasigroup; left linear quasigroup 
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Smith, Jonathan D. H. A class of quasigroups solving a problem of ergodic theory. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 2, pp. 409-414. http://geodesic.mathdoc.fr/item/CMUC_2000__41_2_a17/