Moufang quasigroups


[Thanks to Alar Leibak, aleibak@ioc.ee, for helping to construct this page]

Definition

A quasigroup satisfing the following identities (Moufang's identities)
	((xy)z)x = x[y((ez)x)] 
	y(x(yz)) = [(y(xf))y]z,
	
where e is the local right-handed identity element to y (i.e. ye=y) and f is the local left-handed identity element for y (i.e. fy=y).

Examples

Structure

Representation

Decision problems

Identity problem:
Word problem:

Spectra and growth

Finite spectrum:
Free spectrum:
Growth series:

History/Importance

References

V. D. Belousov, Fundamentals of the theory of quasigroup and loop (in Russian)

Subsystems


    A Catalogue of Algebraic Systems / John Pedersen / jfp@math.usf.edu