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arXiv · 1311.6189

Growth Rates of Algebras, II: Wiegold Dichotomy

Keith A. Kearnes·Emil W. Kiss·Agnes Szendrei
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Abstract

We investigate the function $d_\mathbf{A}(n)$, which gives the size of a least size generating set for $\mathbf{A}^n$, in the case where $\mathbf{A}$ has a cube term. We show that if $\mathbf{A}$ has a $k$-cube term and $\mathbf{A}^k$ is finitely generated, then $d_\mathbf{A}(n) \in O(\log(n))$ if $\mathbf{A}$ is perfect and $d_\mathbf{A}(n) \in O(n)$ if $\mathbf{A}$ is imperfect. When $\mathbf{A}$ is finite, then one may replace "Big Oh" with "Big Theta" in these estimates.

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Keith A. Kearnes, Emil W. Kiss, Agnes Szendrei. 2014-01-11. Growth Rates of Algebras, II: Wiegold Dichotomy. https://doi.org/10.1142/s0218196715500101

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