Some pseudocompact-like properties in certain topological groups

Abstract

We construct in ZFC a countably compact group without non-trivial convergent sequences of size 2c, answering a question of Bellini, Rodrigues and Tomita [4]. We also construct in ZFC a selectively pseudocompact group which is not countably pracompact, showing that these two properties are not equivalent in the class of topological groups. Using the same technique, we construct a group which has all powers selectively pseudocompact but is not countably pracompact, assuming the existence of a selective ultrafilter.