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arXiv · 2512.23674

Groups with fast-growing conjugator length functions

Martin R. Bridson·Timothy R. Riley
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Abstract

We construct the first examples of finitely presented groups whose conjugator length function is exponential; these are central extensions of groups of the form $F_m\rtimes F_2$. Further, we use a fibre product construction to exhibit a family of finitely presented groups $\Gamma_k$ where, for each $k$, the conjugator length function of $\Gamma_k$ grows like functions lying in the $k$-th level of the Grzegorczyk hierarchy of primitive recursive functions.

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Martin R. Bridson, Timothy R. Riley. 2025-12-29. Groups with fast-growing conjugator length functions. https://arxiv.org/abs/2512.23674

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