Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growth Rates of Algebras, II: Wiegold Dichotomy   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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The categories of this paper are: funct-an
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int