TS-quasigroups
[Thanks to Alar Leibak, aleibak@ioc.ee, for helping to construct this page]
Definition
A
quasigroup
where
xy=z
implies the following equalities:
yx=z, xz=y, zx=y, yz=x
and
zy=x
A
quasigroup
satisfying
xy=yx
and
x(xy)=y
Examples
Every Steiner quasigroup
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