In this talk, stating a historical survey in varietal Schur multipliers (the Baer invariant with respect to a variety) of some well-known products of groups, we present recent developments in the subject. More precisely, we talk about (i) a varietal multiplier and capability of finitely generated Abelian groups; (ii) nilpotent multipliers of verbal products of groups; (iii) polynilpotent multipliers of multiple nilpotent products of cyclic groups.

Keywords