  We prove that if there are $\mathfrak c$ incomparable selective ultrafilters
then, for every infinite cardinal $\kappa$ such that $\kappa^\omega=\kappa$,
there exists a group topology on the free Abelian group of cardinality $\kappa$
without nontrivial convergent sequences and such that every finite power is
countably compact. In particular, there are arbitrarily large countably compact
groups. This answers a 1992 question of D. Dikranjan and D. Shakhmatov.
