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arXiv · 1702.06926

On Varietal Capability of Infinite Direct Products of Groups

Hanieh Mirebrahimi·Behrooz Mashayekhy
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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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Hanieh Mirebrahimi, Behrooz Mashayekhy. 2017-02-22. On Varietal Capability of Infinite Direct Products of Groups. https://arxiv.org/abs/1702.06926

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