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21.102 (2026)

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Let $\mathfrak{V}$ be a variety generated by a finite group, and let $f(n)$ be the order of the free group in $\mathfrak{V}$ on $n$ generators. Is it true that the sequence $\sqrt[n]{\log f(n)}$ has a limit as $n \to \infty$, and this limit is an integer?

Contributor: A. Yu. Olshanskii

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