a1 Department of Mathematical and Computational Sciences, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS
a2 Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois, 60115, U.S.A.
For unexplained terms in semigroup theory see  or .
Let C, D be classes of semigroups such that every finite semigroup in the class C is embeddable in a finite semigroup in the class D. If n ≥ 2 then k is said to be a C – D cover of n if every semigroup of order n in the class C is embeddable in a semigroup in the class D of order not greater than k. Let be the least C – D cover of n.
(Received May 11 1990)