Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran
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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Mirebrahimi, H., & Mashayekhy, B. (2012). On varietal capability of Infinite direct products of groups. International Journal of Group Theory, 1(3), 33-37. doi: 10.22108/ijgt.2012.850
MLA
Hanieh Mirebrahimi; Behrooz Mashayekhy. "On varietal capability of Infinite direct products of groups". International Journal of Group Theory, 1, 3, 2012, 33-37. doi: 10.22108/ijgt.2012.850
HARVARD
Mirebrahimi, H., Mashayekhy, B. (2012). 'On varietal capability of Infinite direct products of groups', International Journal of Group Theory, 1(3), pp. 33-37. doi: 10.22108/ijgt.2012.850
VANCOUVER
Mirebrahimi, H., Mashayekhy, B. On varietal capability of Infinite direct products of groups. International Journal of Group Theory, 2012; 1(3): 33-37. doi: 10.22108/ijgt.2012.850
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