Ping-pong for basis-conjugating HNN-extension of free group
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908721044520960 |
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| author | Ionin, Vasily |
| author_facet | Ionin, Vasily |
| contents | We isolate a tractable class of HNN-extensions of a free group, namely, multiple HNN-extensions by basis-conjugating embeddings. For this class, we construct a normal form and establish a practical version of the ping-pong lemma that provides verifiable sufficient conditions for a set of elements to generate a free subgroup.
We then apply these results to the pure braid group $P_{n+1}$, exploiting its well-known decomposition as a semidirect product of free groups. Our approach yields new families of free subgroups within the first two factors $F_n \rtimes F_{n-1}$ of this decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19635 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ping-pong for basis-conjugating HNN-extension of free group Ionin, Vasily Group Theory 20E06, 20F36 We isolate a tractable class of HNN-extensions of a free group, namely, multiple HNN-extensions by basis-conjugating embeddings. For this class, we construct a normal form and establish a practical version of the ping-pong lemma that provides verifiable sufficient conditions for a set of elements to generate a free subgroup. We then apply these results to the pure braid group $P_{n+1}$, exploiting its well-known decomposition as a semidirect product of free groups. Our approach yields new families of free subgroups within the first two factors $F_n \rtimes F_{n-1}$ of this decomposition. |
| title | Ping-pong for basis-conjugating HNN-extension of free group |
| topic | Group Theory 20E06, 20F36 |
| url | https://arxiv.org/abs/2509.19635 |