# A class of quasigroups solving a problem of ergodic theory

Commentationes Mathematicae Universitatis Carolinae (2000)

- Volume: 41, Issue: 2, page 409-414
- ISSN: 0010-2628

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topSmith, Jonathan D. H.. "A class of quasigroups solving a problem of ergodic theory." Commentationes Mathematicae Universitatis Carolinae 41.2 (2000): 409-414. <http://eudml.org/doc/248645>.

@article{Smith2000,

abstract = {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.},

author = {Smith, Jonathan D. H.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {quasigroup; Latin square; Markov chain; doubly stochastic matrix; ergodic; superergodic; dripping faucet; group isotope; central quasigroup; semicentral quasigroup; $T$-quasigroup; left linear quasigroup; pointed quasigroups; Latin squares; Markov chains; doubly stochastic matrices; ergodicity; superergodicity; group isotopes; semicentral quasigroups; left linear quasigroups},

language = {eng},

number = {2},

pages = {409-414},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A class of quasigroups solving a problem of ergodic theory},

url = {http://eudml.org/doc/248645},

volume = {41},

year = {2000},

}

TY - JOUR

AU - Smith, Jonathan D. H.

TI - A class of quasigroups solving a problem of ergodic theory

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2000

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 41

IS - 2

SP - 409

EP - 414

AB - 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.

LA - eng

KW - quasigroup; Latin square; Markov chain; doubly stochastic matrix; ergodic; superergodic; dripping faucet; group isotope; central quasigroup; semicentral quasigroup; $T$-quasigroup; left linear quasigroup; pointed quasigroups; Latin squares; Markov chains; doubly stochastic matrices; ergodicity; superergodicity; group isotopes; semicentral quasigroups; left linear quasigroups

UR - http://eudml.org/doc/248645

ER -

## References

top- Ash R.B., Information Theory, Wiley New York, NY (1965). (1965) Zbl0141.34904MR0229475
- Belyavskaja G.B., Tabarov A.H., The nuclei and center of linear quasigroups (in Russian), Izv. Akad. Nauk Respub. Moldova Mat. 3 (1991), 37-42. (1991) MR1174875
- Belyavskaja G.B., Tabarov A.H., One-sided T-quasigroups and irreducible balanced identities, Quasigroups Related Systems 1 (1994), 8-21. (1994) MR1327942
- Chein O., Pflugfelder H.O., Smith J.D.H. (eds.), Quasigroups and Loops: Theory and Applications, Heldermann Berlin (1990). (1990) Zbl0719.20036MR1125806
- Feller W., An Introduction to Probability Theory and its Applications, Volume I, Wiley New York, NY (1950). (1950) MR0038583
- Horibe Y., On the increase of conditional entropy in Markov chains, in ``Transactions of the Tenth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, Volume A'', Academia, Prague, 1988, pp.391-396. Zbl0707.60059MR1136296
- Ježek J., Kepka T., Quasigroups, isotopic to a group, Comment. Math. Univ. Carolinae 16 (1975), 59-76. (1975) MR0367103
- Němec P., Kepka T., T-quasigroups I, II, Acta Univ. Carolinae - Math. et Phys. 12 (1971), 1 39-49 and no. 2, 31-49. (1971) MR0320206
- Smith J.D.H., Mal'cev Varieties, Springer Berlin (1976). (1976) Zbl0344.08002MR0432511
- Smith J.D.H., Romanowska A.B., Post-Modern Algebra, Wiley New York, NY (1999). (1999) Zbl0946.00001MR1673047

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