Abstract
We investigate the function dA(n), which gives the size of a least size generating set for An, in the case where A has a cube term. We show that if A has a k-cube term and Ak is finitely generated, then dA(n) ∈ O( log (n)) if A is perfect and dA(n) ∈ O(n) if A is imperfect. When A is finite, then one may replace "Big O" with "Big Theta" in these estimates.
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