Metrizable refinements of group topologies and the pseudo-intersection number

The pseudo-intersection number, denoted p , is the minimum cardinality of a family A ⊆ P ( ω ) having the strong finite intersection property but no infinite pseudo-intersection. For every countable topologizable group G, let p G denote the minimum character of a nondiscrete Hausdorff group topology on G which cannot be refined to a nondiscrete metrizable group topology. We show that p G = p .