FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 6, PAGES 33-39

**Groupoids with the identity defining the commutative Moufang loops**

G. B. Belyavskaya

A. Kh. Tabarov

Abstract

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

Location: http://mech.math.msu.su/~fpm/eng/k08/k086/k08602h.htm

Last modified: June 4, 2009