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arXiv · 2507.21505

Conjugator Length in the Baumslag-Gersten Group

Conan Gillis
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Abstract

We show that the conjugator length function of the Baumslag-Gersten group is equivalent to a tower of exponentials of height $\lfloor \log_2n\rfloor$ -- in particular it grows faster than any tower of exponentials of fixed height. We ask whether any one-relator group has a larger conjugator length function than the Baumslag-Gersten group. Along the way, we also show that the conjugator length function of the $m$-th iterated Baumslag-Solitar groups is equivalent to the $(m-1)$-times iterated exponential function.

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Conan Gillis. 2025-07-29. Conjugator Length in the Baumslag-Gersten Group. https://arxiv.org/abs/2507.21505

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