Abelian groups admitting a Fréchet–Urysohn pseudocompact topological group topology

We show that every Abelian group GG with r0(G)=|G|=|G|ωr0(G)=|G|=|G|ω admits a pseudocompact Hausdorff topological group topology TT such that the space (G,T)(G,T) is Fréchet–Urysohn. We also show that a bounded torsion Abelian group GG of exponent nn admits a pseudocompact Hausdorff topological group topology making GG a Fréchet–Urysohn space if for every prime divisor pp of nn and every integer k≥0k≥0, the Ulm–Kaplansky invariant fp,kfp,k of GG satisfies (fp,k)ω=fp,k(fp,k)ω=fp,k provided that fp,kfp,k is infinite and fp,k>fp,ifp,k>fp,i for each i>ki>k.Our approach is based on an appropriate dense embedding of a group GG into a ΣΣ-product of circle groups or finite cyclic groups.