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
Any
group
Any Moufang loop
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