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Theoretical analysis demonstrates finite generation of pro-supersolvable closures in free group subgroups, extending established pro-p and nilpotent theorems.
We prove that the pro-(finite supersolvable) closure of a finitely generated subgroup of the free group is finitely generated. This extends similar results for pro-𝑝 closures proved by Ribes–Zalesskii and pro-(finite nilpotent) closures proved by Margolis–Sapir–Weil.
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Chen et al. (2026) studied this question.
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