TS-quasigroups


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

Definition

  1. A quasigroup where xy=z implies the following equalities:
    
    	 yx=z,  xz=y,  zx=y,  yz=x and zy=x
    	
  2. A quasigroup satisfying
    	xy=yx   and   x(xy)=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