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arXiv · 2311.01668

Elliptic subgroups in cyclic splittings of a free group

Brent B. Solie
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Abstract

We use Gersten's generalization of Whitehead's algorithm to determine whether a given finitely generated subgroup of a free group $F$ is elliptic in an elementary cyclic splitting of $F$. We provide a similar result for all elementary cyclic splittings of a free group of rank two and partial results towards an algorithm for ellipticity in elementary cyclic splittings of $F$ as an HNN-extension.

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Brent B. Solie. 2023-11-03. Elliptic subgroups in cyclic splittings of a free group. https://arxiv.org/abs/2311.01668

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