On varietal capability of Infinite direct products of groups

Document Type: Research Paper

Authors

Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran

Abstract

Recently‎, ‎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.

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