Subgroups of a free group with every growth rate

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arxiv 2505.10650 v1 pith:GVK4UEYS submitted 2025-05-15 math.GR

Michail Louvaris , Daniel T. Wise , Gal Yehuda This is my paper · ORCID

classification math.GR

keywords alphaeverygrowthrateexistsfreegroupsubgroup

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abstract

For every $\alpha \in [1,2r-1]$, we show there exists a subgroup $H<F_r$ whose growth rate is $\alpha$.

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Critical-exponent stratification and inverse realization on biregular trees
math.GR 2026-07 accept novelty 7.0 of 10

Free type-preserving actions on biregular trees realize every critical exponent up to (1/2)log(rs); finitely generated actions have a countable dense spectrum, and rank-two values equal roots of three explicit polynom...