Abstract: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.
| Subjects: | Group Theory (math.GR) |
| Cite as: | arXiv:2605.24772 [math.GR] |
| (or arXiv:2605.24772v1 [math.GR] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24772 arXiv-issued DOI via DataCite (pending registration) |
From: Jean-Luc Rabideau [view email]
[v1]
Sat, 23 May 2026 23:15:22 UTC (21 KB)
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