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arXiv · 2506.01248

Conjugacy in a family of free-by-cyclic groups

Martin R. Bridson·Timothy R. Riley·Andrew W. Sale
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Abstract

We analyse the geometry and complexity of the conjugacy problem in a family of free-by-cyclic groups $H_m=F_m\rtimes\mathbb{Z}$ where the defining free-group automorphism is positive and polynomially growing. We prove that the conjugator length function of $H_m$ is linear, and describe polynomial-time solutions to the conjugacy problem and conjugacy search problem in $H_m$.

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Martin R. Bridson, Timothy R. Riley, Andrew W. Sale. 2025-06-02. Conjugacy in a family of free-by-cyclic groups. https://arxiv.org/abs/2506.01248

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