IP-quasigroups


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

Definition

A quasigroup with two additional unary operations (I and J), such that the following identities hold:
	I(x)(xy) = y   and  (yx)J(x) = 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 quasigroups and loops (in Russian)

Subsystems


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