Subgroup Conjugacy Separability in Residually Free Groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910835701448704 |
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| author | Chagas, S. C. Kazachkov, I. |
| author_facet | Chagas, S. C. Kazachkov, I. |
| contents | We prove that finitely presented residually free groups are subgroup conjugacy separable. Furthermore, if they are of type $FP_\infty$, then they are also subgroup conjugacy distinguished.
Using a connection between conjugacy separability and residual finiteness of outer automorphism group established by Grossman in \cite{Grossman}, we show that finitely presented residually free groups have residually finite outer automorphism groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13726 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Subgroup Conjugacy Separability in Residually Free Groups Chagas, S. C. Kazachkov, I. Group Theory 20E26, 20E18, 20F67 We prove that finitely presented residually free groups are subgroup conjugacy separable. Furthermore, if they are of type $FP_\infty$, then they are also subgroup conjugacy distinguished. Using a connection between conjugacy separability and residual finiteness of outer automorphism group established by Grossman in \cite{Grossman}, we show that finitely presented residually free groups have residually finite outer automorphism groups. |
| title | Subgroup Conjugacy Separability in Residually Free Groups |
| topic | Group Theory 20E26, 20E18, 20F67 |
| url | https://arxiv.org/abs/2502.13726 |