On the Hilbert–Poincaré series of graded algebras associated with groups

A description is given of groups for which the coefficients of the Hilbert–Poincaré series of the associated algebra have power growth. Examples of finitely generated $p$-groups for which the growth of the coefficients of the Hilbert–Poincaré series is of order $e^{\sqrt n}$ are constructed. The results are applied to the theory of degrees of growth of groups.
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