  A space X is selectively sequentially pseudocompact if for every sequence
(U_n) of non-empty open subsets of X, one can choose a point x_n in each U_n in
such a way that the sequence (x_n) has a convergent subsequence. Let G be a
group from one of the following three classes: (i) V-free groups, where V is an
arbitrary variety of Abelian groups; (ii) torsion Abelian groups; (iii)
torsion-free Abelian groups. Under the Singular Cardinal Hypothesis SCH, we
prove that if G admits a pseudocompact group topology, then it can also be
equipped with a selectively sequentially pseudocompact group topology. Since
selectively sequentially pseudocompact spaces are strongly pseudocompact in the
sense of Garc\'ia-Ferreira and Ortiz-Castillo, this provides a strong positive
(albeit partial) answer to a question of Garc\'ia-Ferreira and Tomita.
