[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"QudnMRKmZL":3},"# odd-order\n\nEnglish | [日本語](README.ja.md)\n\nA complete formalization of the **Feit–Thompson Odd Order Theorem** in **Lean 4 + mathlib** — *every finite group of odd order is solvable* — together with the finite group theory it is built on.\n\n```lean\ntheorem feitThompson {G : Type*} [Group G] [Finite G] (hodd : Odd (Nat.card G)) :\n    IsSolvable G\n```\n\n## Status\n\n**The Odd Order Theorem is proved and axiom-clean** (2026-07-15):\n\n```\n#print axioms OddOrder.feitThompson\n-- 'OddOrder.feitThompson' depends on axioms: [propext, Classical.choice, Quot.sound]\n```\n\nNo `sorryAx`, no project-specific axioms — only Lean's three standard ones.\n\nThe project is now in its second phase: **formalizing the three source textbooks in full**, not merely\nthe path through them that the Odd Order Theorem needs.\n\n> ✅ **The Lean sources (`OddOrder/`) are `sorry`-free as of 2026-08-07.** The last one to go was the\n> `Q₈` case of the Brauer–Suzuki theorem — cited by the sources, proved in none of them. Closing it\n> meant building modular character theory from scratch (`p`-modular systems, Brauer characters,\n> blocks, defect groups, Brauer's three main theorems), following Navarro's *Characters and Blocks of\n> Finite Groups*, Ch. 1–7. Note that `sorry`-free is *not* the same as \"the three books are done\":\n> a result that has not been stated yet produces no `sorry`. Coverage is tracked separately, below.\n\n## Beyond the Feit–Thompson theorem: a finite group theory library\n\nProving Feit–Thompson requires a large body of finite group theory that mathlib does not yet have.\nThat theory makes up the bulk of this repository, and completing it is now a goal in its own right:\n\n- **Isaacs**, *Finite Group Theory* (AMS GSM 92, 2008) — the general prerequisites: the Fitting subgroup,\n  Hall subgroups and π-separability, coprime action, Frobenius groups, transfer, the Thompson subgroup\n  and ZJ, the generalized Fitting subgroup `F*(G)`.\n- **Bender–Glauberman**, *Local Analysis for the Odd Order Theorem* (LMS LNS 188, 1994) — the local\n  analysis and the final contradiction.\n- **Peterfalvi**, *Character Theory for the Odd Order Theorem* (LMS LNS 272, 2000) — the\n  character-theoretic half: the Dade isometry, coherence, and the exceptional-character arguments.\n- **Gorenstein**, *Finite Groups* (1968) — **in part only**. Bender–Glauberman repeatedly defers proofs\n  to Gorenstein (\"**G**, Thm X.Y.Z\"), most visibly around p-stability, ZJ, and small-rank p-groups,\n  and Peterfalvi's Appendix C likewise cites Gorenstein for the Brauer–Suzuki theorem (Ch. 12). Where\n  such a citation is not already covered by Isaacs or by mathlib, the Gorenstein proof is written out\n  here (Theorems 3.4, 3.7/3.8/3.10, 4.15, 5.3.9–5.3.13, 7.6.5, Brauer–Suzuki for `|S| ≥ 16`, among\n  others, under `OddOrder/BG/` and `OddOrder/GroupTheory/`). Gorenstein is *not* being formalized as\n  a book.\n\nThree bodies of proof come from outside these books altogether: the books state the results but take\nthe proofs from the original literature, so the sources themselves are formalized here.\n\n- **Higman**, \"Suzuki 2-groups\" (*Illinois Journal of Mathematics* 7, 1963). Peterfalvi's Appendix III\n  restates Higman's classification of Suzuki 2-groups but explicitly takes its proof from the paper;\n  that proof is formalized in full under [`OddOrder/Higman/`](OddOrder/Higman/) — about 65,000\n  `sorry`-free lines, the largest single item in the library.\n- **Navarro**, *Characters and Blocks of Finite Groups* (LMS LNS 250, 1998), Ch. 1–7. The `Q₈` case of\n  Brauer–Suzuki is in none of the four books above: Gorenstein's Ch. 12 proves only `|S| ≥ 16` and\n  states the order-8 case without proof (\"all known proofs require the theory of modular characters\" —\n  a theory the book never develops), and mathlib has no modular representation theory at all. So it is\n  built here from the ground up under\n  [`OddOrder/GroupTheory/RepresentationTheory/Modular/`](OddOrder/GroupTheory/RepresentationTheory/Modular/)\n  — `p`-modular systems, Brauer characters, decomposition and Cartan matrices, blocks and defect\n  groups, the Brauer homomorphism and Brauer's three main theorems — about 29,000 lines feeding the\n  character-theoretic argument of Navarro pp. 139–146.\n- **Huppert**, *Endliche Gruppen I* (1967), Kapitel II, Satz 3.2: a solvable 2-transitive permutation\n  group has an elementary abelian regular normal subgroup. Needed by Peterfalvi's Appendix C.\n\nCoverage of the three books is tracked result by result — separately from the `sorry` count, which\nmeasures something else entirely. An audit on 2026-07-16 enumerated all **815 numbered results**:\n470 formalized at full book strength, 78 covered completely by mathlib itself,\n54 present in a specialized form awaiting generalization, and 213 remaining work items. That survey\n([`notes/meta/three_books_full_survey_2026_07_16.md`](notes/meta/three_books_full_survey_2026_07_16.md))\nis a snapshot of the phase-two starting point, not a live scope document — later spot checks found some\nof its per-chapter labels unreliable. Current scope and progress are tracked in the git history and in\n`issues/`, with each item re-verified against the tree before work starts.\n\nEverything sits under the `OddOrder` namespace rather than being upstreamed piecemeal, but mathlib\nnaming and style conventions are followed throughout so that the general-purpose parts stay\nupstreamable later. The tree builds with zero non-`sorry` warnings under mathlib's standard linter\nset, enforced as a strict gate in CI.\n\n## Building\n\n```bash\nlake exe cache get     # prebuilt mathlib oleans (first checkout, and after a mathlib bump)\nlake build OddOrder\n```\n\nThe Lean toolchain is pinned in [`lean-toolchain`](lean-toolchain) and the mathlib revision in\n[`lakefile.toml`](lakefile.toml). A full build is roughly 5,450 jobs.\n\n## Repository layout\n\n| Path | Contents |\n|---|---|\n| [`OddOrder/`](OddOrder/) | The Lean sources (~1,680 files, ~830,000 lines). `Isaacs/`, `BG/`, `Peterfalvi/` mirror the three books; `Higman/` holds the Suzuki 2-groups paper; `GroupTheory/`, `Algebra/`, `Mathlib/` hold general-purpose material, including `GroupTheory/RepresentationTheory/Modular/` for the block theory |\n| [`OddOrder/FeitThompson.lean`](OddOrder/FeitThompson.lean) | The main theorem and the minimal-counterexample reduction |\n| [`OddOrder/AxiomsCheck.lean`](OddOrder/AxiomsCheck.lean) | Build-time axiom audit of every load-bearing result |\n| [`ROADMAP.md`](ROADMAP.md) | Long-range plan, phases, dependency graph, per-chapter checklists |\n| [`CLAUDE.md`](CLAUDE.md) | Working conventions, and the contributor guide (`AGENTS.md` is a symlink to it) |\n| `notes/` | Per-chapter roadmaps, design decisions, and source-text investigations |\n| `issues/` | File-based issue tracker (`issues/` open, `pending/`, `closed/`) |\n| `coq/` | Submodule: [math-comp/odd-order](https://github.com/math-comp/odd-order), the Coq/mathcomp formalization — a **read-only reference**, consulted because its comments fill in steps the textbooks elide. Nothing is translated from it |\n| `references/` | Textbook PDFs, page images, and extracted text — a submodule pointing at a separate private repository, so the exact revision used is recorded. Not needed to build: CI does not fetch submodules |\n\n## Use of AI\n\nThis project is driven by AI agents: nearly all of the Lean code, notes, and documentation is\nwritten by AI, and **not all of it is human-reviewed**. Proof correctness does not depend on that\nreview: the Lean kernel machine-checks every proof, and the axiom audit\n([`OddOrder/AxiomsCheck.lean`](OddOrder/AxiomsCheck.lean)) pins down exactly what each result\ndepends on. Where reader skepticism remains\nwarranted is the *statements*: whether a Lean declaration faithfully renders the textbook theorem it\ncites. Docstrings carry the book numbering precisely so that this correspondence can be checked.\n\n## License\n\nApache License 2.0 — see [LICENSE](LICENSE).\n",1786349528243]