Conjugacy in a family of free-by-cyclic groups

2025/06/02 by Martin R. Bridson, Bridson, Martin R., Tim Riley +3 · 2 citations
Mathematics · Materials Science · #Mathematics and Applications #Synthesis and properties of polymers

paper · pdf · doi:10.48550/arxiv.2506.01248

Abstract

We analyse the geometry and complexity of the conjugacy problem in a family of free-by-cyclic groups H_m=F_m\rtimesℤ 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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• Residual finiteness properties of some of Halls groups
• Conjugator length of locally compact groups of Euclidean isometries

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