Cyclic entropic quasigropups

• Autorzy: Bińczak G. , Kaleta J.
• Języki publikacji: EN

Abstrakty

EN

In this paper we explain the relationship of some entropic quasigroups to abelian groups with involution. It is known that (Zn, -n) are examples of cyclic entropic quasigroups which are not groups. We describe all cyclic entropic quasigroups with quasiidentity.

Słowa kluczowe

EN

abelian groups; entropic quasigroups

PL

grupa abelowa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 2
• Strony: 269--281
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Bińczak G.

autor

Kaleta J.

• Faculty of Mathematics and Information Science Warsaw University of Technology Pl. Politechniki 1 00-661 Warszawa, Poland,

Bibliografia

• [1] G. Bińczak, J. Kaleta, The table of characters of some quasigroups, Discussiones Mathematicae General Algebra and Applications 27 (2007), 147-167.
• [2] O. Chein, H. O. Pflugfelder, J. D. H. Smith, Quasigroups and Loops: Theory and Applications, Berlin (1990).
• [3] V. J. Havel, A. Vanžurova, Medial Quasigroups and Geometry, Olomouc (2006).
• [4] D. C. Murdoch, Structure of abelian quasigroups, Trans. Amer. Math. Soc. 49 (1941), 392-409.
• [5] J. D. H. Smith, Representation Theory of Infinite Groups and Finite Quasigroups, Universite de Montreal, 1986.
• [6] K. Toyoda, "On axioms of mean transformations and automorphic transformations of abelian groups, Tōohoku Math. J. 46 (1940), 239-251.
• [7] K. Toyoda, On affine geometry of abelian groups, Proc. Imp. Acad. Tokyo 16 (1940), 161-164.