  We study algebraic and topological properties of topological semigroups
containing a copy of the bicyclic semigroup C(p,q). We prove that each
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) Tychonov semigroup containing a copy of
C(p,q).
