It was an old problem of van Dowen the existence of a countably compact topological group without non-trivial convergent sequences, which was finally solved in the positive by Hrusak, van Mill, Ramos-García and Shelah, in 2021. In their paper, besides the aforementioned result, the authors introduced a contruction of a p-compact topological group without non-trivial convergent sequences by means of iterated ultrapowers of the countable boolean group, where p is a selective ultrafilter, and left several open questions related to this contruction. In the present talk we will review some of such questions.