University of IsfahanInternational Journal of Group Theory2251-76501320120901On varietal capability of Infinite direct products of groups333785010.22108/ijgt.2012.850ENHaniehMirebrahimiDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic
Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, IranBehroozMashayekhyDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic
Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, IranJournal Article20120507Recently, the authors gave some conditions under which a direct product of finitely many groups is $\mathcal{V}-$capable if and only if each of its factors is $\mathcal{V}-$capable for some varieties $\mathcal{V}$. In this paper, we extend this fact to any infinite direct product of groups. Moreover, we conclude some results for $\mathcal{V}-$capability of direct products of infinitely many groups in varieties of abelian, nilpotent and polynilpotent groups.https://ijgt.ui.ac.ir/article_850_c7158d00eaa639c32430a262f09c81fa.pdf