Injectives in varieties of completely simple semigroups (Q1068206)

The varieties of bands that are subvarieties of the variety \({\mathcal C}{\mathcal S}\) of all completely simple semigroups are the varieties of rectangular bands. It is easy to see that each member of a variety of rectangular bands is an injective in that variety. Furthermore, the injectives in \({\mathcal C}{\mathcal S}\) are precisely the rectangular bands. The injectives in varieties of groups are known. The aim here is to characterize the injectives in any subvariety of \({\mathcal C}{\mathcal S}\). There are subvarieties with non-band and non-group injectives.