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Conjugacy in a family of free-by-cyclic groups
Martin Bridson, Timothy Riley, and Andrew Sale 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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