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On almost nilpotent varieties of subexponential growth. (English) Zbl 1333.17001

Summary: Let \({}_2\mathcal{N}\) be the variety of left-nilpotent algebras of index two, that is the variety of algebras satisfying the identity \(x(y z) \equiv 0\). We introduce two new varieties, denoted by \(\mathcal{V}_{\mathit{sym}}\) and \(\mathcal{V}_{\mathit{alt}}\), contained in the variety \({}_2\mathcal{N}\) and we prove that \(\mathcal{V}_{\mathit{sym}}\) and \(\mathcal{V}_{\mathit{alt}}\) are the only two varieties almost nilpotent of subexponential growth.

MSC:

17A30 Nonassociative algebras satisfying other identities
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