A semiband is defined as a semigroup generated by idempotents. It is known that every finite semigroup is embeddable in a finite semiband. For a class C of semigroups and an integer n≧2, the number σC (n) is defined as the smallest k with the property that every semigroup of order n in the class C is embeddable in a semiband of order not exceeding k. It is shown that for the class Gp of groups σGp(n) = nq(ρGp(n)), where
and
Estimates are known (and are quoted) for the function q. Estimates are considered for the function pC for various C
It is shown also that if C0S, CS denote respectively the classes of completely 0-simple and completely simple semigroups, then