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13.52 (1995)

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The dimension of a finitely based variety of algebras $\mathfrak{V}$ is defined to be the maximal length of a basis (that is, an independent generating set) of the $SC$-theory $SC(\mathfrak{V})$, which consists of the strong Mal’cev conditions satisfied on $\mathfrak{V}$. The dimension is defined to be infinite if the lengths of bases in $SC(\mathfrak{V})$ are not bounded. Does every finite abelian group generate a variety of finite dimension?

Contributor: D. M. Smirnov

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