Geodesic
On growth of varieties of commutative linear algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 5, pp. 165-170.

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There exists a varieties of commutative linear algebras over a field of zero characteristic whose exponent is equal to $\alpha$ for any real $\alpha>1$ and the intermediate growth is $n^{n^\beta}$ for any real $0\beta1$. 
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S. S. Mishchenko. On growth of varieties of commutative linear algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 5, pp. 165-170. http://geodesic.mathdoc.fr/item/FPM_2008_14_5_a10/

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