Embedding the bicyclic semigroup into countably compact topological semigroups

We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C ( p , q ) . We prove that a topological semigroup S with pseudocompact square contains no dense copy of C ( p , q ) . On the other hand, we construct a (consistent) example of a pseudocompact (countably compact) Tychonoff semigroup containing a copy of C ( p , q ) .