The Join of Orthogroup Variety and Cryptogroup Variety

A subvariety of the variety of completely regular semigroups is defined by the identity((x0y0)0z0)0 =(x0(y0z0)0)0.An example is provided to illustrate that the subvariety is proper.Two additional identities,x(yz)0x(yz)0=(yz0)0x(yz)0and(xy)0z(xy)0z=(xy)0z(x0y)0z,are used to define a subvariety of the above subvariety.Examples are given to show that the above three identities are independent on each other.It is proved that the proper subvariety defined by the three identities is the join of the orthogroup variety and the cryptogroup variety.