Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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.  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.
['Keith A. Kearnes', 'Emil W. Kiss', 'Ágnes Szendrei']
I am writing a research paper on a idea Growth Rates of Algebras, II: Wiegold Dichotomy
[{"from": "human", "value": "I am writing a research paper on a idea Growth Rates of Algebras, II: Wiegold Dichotomy"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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.  show that if A has a k-cube term and Ak is finitely generated, then dA(n) \u2208 O(log(n)) if A is perfect and dA(n) \u2208 O(n) if A is imperfect. When A is finite, then one may replace \"Big O\" with \"Big Theta\" in these estimates."}]