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