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On varietal capability of Infinite direct products of groups | ||
| International Journal of Group Theory | ||
| مقاله 5، دوره 1، شماره 3، آذر 2012، صفحه 33-37 اصل مقاله (382.01 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2012.850 | ||
| نویسندگان | ||
| Hanieh Mirebrahimi* ؛ Behrooz Mashayekhy | ||
| Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Capable group؛ Direct product؛ Variety of groups؛ V−capable group؛ direct limit | ||
| مراجع | ||
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