{"paper":{"title":"Key subgroups in the Polish group of all automorphisms of the rational circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.GN"],"primary_cat":"math.DS","authors_text":"Michael Megrelishvili","submitted_at":"2024-10-23T14:25:56Z","abstract_excerpt":"Extending some results of a joint work with E. Glasner, we continue to study the Polish group $G:=\\mathrm{Aut}(\\mathbb{Q}_0)$ of all circular order preserving permutations of the rational circle $\\mathbb Q_0=\\mathbb Q/\\mathbb Z$, endowed with the pointwise topology. We show that the point stabilizers $H=G_q$ are extremely amenable inj-key subgroups of $G$ (that is, they distinguish coarser Hausdorff group topologies on $G$), but are not co-minimal in $G$. These examples answer a question posed in a joint work with M. Shlossberg and are inspired by a question of V. Pestov concerning Polish grou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.17905","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.17905/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}