Conjugator Length in the Baumslag-Gersten Group
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911081600909312 |
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| author | Gillis, Conan |
| author_facet | Gillis, Conan |
| contents | We show that the conjugator length function of the Baumslag-Gersten group is bounded above and below by a tower of exponentials of logarithmic height -- in particular it grows faster than any tower of exponentials of fixed height. We conjecture that no 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 $m$-times iterated exponential function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21505 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conjugator Length in the Baumslag-Gersten Group Gillis, Conan Group Theory We show that the conjugator length function of the Baumslag-Gersten group is bounded above and below by a tower of exponentials of logarithmic height -- in particular it grows faster than any tower of exponentials of fixed height. We conjecture that no 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 $m$-times iterated exponential function. |
| title | Conjugator Length in the Baumslag-Gersten Group |
| topic | Group Theory |
| url | https://arxiv.org/abs/2507.21505 |