G. B. Belyavskaya, A. Kh. Tabarov, “Groupoids with the identity defining the commutative Moufang loops”, Fundam. Prikl. Mat., 2008, Volume 14, Issue 6,Pages <nobr>33

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Groupoids with the identity defining the commutative Moufang loops

G. B. Belyavskaya^a, A. Kh. Tabarov^b

^a Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Kishinev
^b Tajik State University, Dushanbe

Abstract: It is known that in the class of loops the identity $xy\cdot xz=x^2\cdot yz$ defines the commutative Moufang loops. In the article, we consider groupoids with this identity and establish properties of some classes of such groupoids.

UDC: 512.548