The least cardinal λ such that some (equivalently: every) compact group with weight α admits a dense, pseudocompact subgroup of cardinality λ is denoted by m(α). Clearly, $m\left(\alpha \right)\le 2^{\alpha }$. We show:    Theorem 4.12. Let G be Abelian with |G| = γ. If either m(α) ≤ α and m$\left(\alpha \right)\le r_0\left(G\right)\le \gamma \le 2^{\alpha }$, or α > ω and ${\alpha }^{\omega }\le r_0\left(G\right)\le 2^{\alpha }$, then G admits a pseudocompact group topology of weight α.  Theorem 4.15. Every connected, pseudocompact Abelian group G with wG = α ≥ ω satisfies $r_0\left(G\right)\ge m\left(\alpha \right)$.  Theorem 5.2(b). If G is divisible Abelian with $2^{r_0\left(G\right)}\le \gamma$, then G admits at most $2^{\gamma }$-many...

We construct in Bell-Kunen’s model: (a) a group maximal topology on a countable infinite Boolean group of weight ${\aleph }_1<ℭ$ and (b) a countable irresolvable dense subspace of $2^{{\omega }_1}$. In this model $ℭ={\aleph }_{{\omega }_1}$.