{
  "schema_version": 1,
  "problem_number": "AIM-DYNAMICAL_SYSTEMS-0011",
  "title": "Maximal Finite-Set Stabilizers in Thompson's Group T",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "Let D = Z[1/2]/Z be the dyadic circle and let T be Thompson's orientation-preserving circle group. We prove that, for every nonempty finite set A contained in D, its setwise stabilizer is a maximal proper subgroup of countably infinite index in T. If |A| = k, then Stab_T(A) is isomorphic to F^k semidirect C_k, equivalently the regular wreath product F wr C_k, where the cyclic group permutes the factors. Stabilizers with the same cardinality are conjugate, whereas those with distinct cardinalities are pairwise nonisomorphic. The proof establishes a general circular-order criterion: a group with the finite circular extension property acts primitively on the k-element subsets for every k. This yields a countably infinite family of maximal infinite-index subgroups and supplies examples requested in the 2024 AIM problem list on groups of dynamical origin. The theorem is apparently unrecorded in the literature checked; no absolute priority claim is made.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.GR"
  ],
  "keywords": [
    "Thompson group T",
    "maximal subgroups",
    "primitive actions",
    "finite-set stabilizers",
    "circular orders",
    "wreath products",
    "maximal subgroup",
    "primitive action",
    "finite-set stabilizer",
    "circular order",
    "AIM-DYNAMICAL_SYSTEMS-0011",
    "open mathematics",
    "mathematical proof",
    "math.GR"
  ],
  "manuscript_version_date": "2026-09-04",
  "publication_date": "2026-09-05",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-09-05",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-dynamical-systems-0011/",
  "pdf_url": "https://eulersolve.org/papers/aim-dynamical-systems-0011/paper.pdf?v=ef1eca13d92d",
  "doi": "10.5281/zenodo.22324898",
  "zenodo_record_url": "https://zenodo.org/records/22324898",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": null,
  "files": {
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      "sha256": "ef1eca13d92d3447e96d2550a4d06f3e9993ca62beb8642f3345c2382faa151e"
    },
    "source.zip": {
      "sha256": "59d081a81b33006c01637236a24ceee0c4670d79c4e8f68dc8482bef351346e7"
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    "verification_report.md": {
      "sha256": "36244fded214f3b7993e96a0d931430dcaf62a39470e58c49d579bf5807f0657"
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  },
  "ai_use_disclosure": "AI-assisted tools supported literature search, computation, proof auditing, and manuscript preparation. The author remains responsible for all claims and the final text."
}