Subsemigroups of completely simple semigroups (Q802759)

A semigroup which is embeddable into a completely simple semigroup satisfies some weak cancellation laws (C). Conversely, if S is a semigroup which generates a variety which does not contain the variety of left regular bands, nor the variety of right regular bands, then S is embeddable into a completely simple semigroup if it satisfies the laws (C). This result is used to characterize the subsemigroups of completely simple semigroups over nilpotent groups of class n.