Realizing Non-Archimedean Polish Groups as Outer Automorphism Groups
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914597141741568 |
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| author | Rabideau, Jean-Luc |
| author_facet | Rabideau, Jean-Luc |
| contents | We show that every non-Archimedean Polish group $P$ is the outer automorphism group of a countable discrete group $G_P$. Moreover, our construction provides a Borel map $f$ from the Effros space of closed subgroups of the permutation group $S_\infty$ to the space of normal subgroups of the countably-generated free group $F_\infty$ such that $G_P = F_\infty/f(P)$. The proof relies on small cancellation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24772 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Realizing Non-Archimedean Polish Groups as Outer Automorphism Groups Rabideau, Jean-Luc Group Theory We show that every non-Archimedean Polish group $P$ is the outer automorphism group of a countable discrete group $G_P$. Moreover, our construction provides a Borel map $f$ from the Effros space of closed subgroups of the permutation group $S_\infty$ to the space of normal subgroups of the countably-generated free group $F_\infty$ such that $G_P = F_\infty/f(P)$. The proof relies on small cancellation theory. |
| title | Realizing Non-Archimedean Polish Groups as Outer Automorphism Groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2605.24772 |