Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

A semigroup embedding problem and an arithmetical function

John M. Howiea1 and J. L. Selfridgea2

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 [1] or [4].

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 CD 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 S0305004100069747_inline001 be the least CD cover of n.

(Received May 11 1990)