Subgroups of σ-pseudocompact groups and the ccc

Determine whether every subgroup of a σ-pseudocompact topological group has the countable chain condition (ccc).

Background

The authors prove that every σ-pseudocompact group has calibre (ω1, ω1, 2), hence is ccc (Corollary 4.12). They also show that groups with a K(M)-ordered compact cover, for separable metrizable M, are ccc (Corollary 4.13).

Whether this ccc property extends to all subgroups of σ-pseudocompact groups remains unresolved, motivating this question.