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Groups with fast-growing conjugator length functions
Martin Bridson and Timothy Riley
We construct the first examples of finitely presented groups where the 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 in the $k$-th level of the Grzegorczyk hierarchy of primitive recursive functions.
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