Abstract
We show that the existence of two incomparable selective ultrafilters imply the existence of two groups H and G such that for every cardinal κ, H κ and G κ are countably compact but H× G is not countably compact. In other words, the existence of two incomparable selective ultrafilters shows that the Comfort group order is not downward directed, answering in the affirmative Question 482 posed by Garcia-Ferreira in the paper of Comfort in the Open Problems in Topology.
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