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feat: add six finite-group-theory benchmark problems#64

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kim-em merged 2 commits intomainfrom
add-cfsg-and-brauer-problems
May 1, 2026
Merged

feat: add six finite-group-theory benchmark problems#64
kim-em merged 2 commits intomainfrom
add-cfsg-and-brauer-problems

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@kim-em kim-em commented May 1, 2026

This PR adds six benchmark statements at the boundary of finite group theory and representation theory: Brauer's theorem on cyclotomic character values, an existential M₂₃ tensor-square problem in the same style as the existing exceptional-Lie tensor-square problems, and four CFSG-adjacent results — Frobenius's kernel-is-normal theorem, Glauberman's Z*, Schreier's conjecture, and the order-restriction part of the classification of 5-transitive permutation groups.

Each statement was checked adversarially before commit. Notable choices:

  • Brauer (brauer_character_in_cyclotomic): asserts ∃ φ : ℚ(ζ_exp G) →+* ℂ, ∀ g, tr(ρ g) ∈ φ.range. The docstring is explicit that this is the character-value form, which is strictly weaker than the full splitting-field statement (every irrep has a ℚ(ζₙ)-form). The latter would need scalar-extension scaffolding mathlib doesn't expose cleanly.
  • M₂₃ (m23_irrep_tensor_square_decomp): existential for a finite group of order 10 200 960 with a 22-dim irrep whose tensor square has 4 isotypic components. Both MonoidAlgebra ℂ G actions (on V and on V ⊗ V) are explicit binders with IsScalarTower, and the V ⊗ V action is pinned by the diagonal-action equation g • (v ⊗ w) = (g • v) ⊗ (g • w) for g : G. The statement does not pin M₂₃ uniquely, but constructing any witness is essentially equivalent to constructing M₂₃.
  • Frobenius (frobenius_kernel_isNormal): explicit 2 ≤ |X| to make the Frobenius-action package fully nondegenerate.
  • Glauberman (glauberman_zStar): uses the global isolated-involution form (no distinct conjugate of t commutes with t); the conclusion form ∀ g, g·t·g⁻¹·t⁻¹ ∈ N is exactly "t central in G/N".
  • Schreier (schreier_conjecture): a local innNormal instance proves Inn(S) ⊴ Aut(S) (one-line simp after ext) so the quotient MulAut S ⧸ MulAut.conj.range typechecks.
  • 5-transitive (five_transitive_card_classification): 5 ≤ |X| defeats vacuity (otherwise C₃ on Fin 3 qualifies); the n!/2 branch is gated by 7 ≤ n since Aₙ is only 5-transitive for n ≥ 7. Title is "Possible orders of …" rather than "Classification of …" since only orders are formalized.

🤖 Prepared with Claude Code

kim-em and others added 2 commits May 1, 2026 15:17
This PR adds six benchmark statements at the boundary of finite group
theory and representation theory: Brauer's theorem on cyclotomic
character values, an existential M_23 tensor-square problem, and four
CFSG-adjacent results (Frobenius's kernel-is-normal theorem, Glauberman's
Z*, Schreier's conjecture, and the order-restriction part of the
classification of 5-transitive permutation groups).

Each statement was checked adversarially before commit: the M_23 problem
pins the diagonal action via an explicit equation rather than a sorry'd
helper instance, the 5-transitive disjunction has 5 ≤ |X| to defeat
vacuity and 7 ≤ n on the n!/2 branch, the Schreier file proves
normality of Inn(S) ⊴ Aut(S) so the quotient typechecks, and the
Brauer docstring is honest that this is the character-value statement
(strictly weaker than the splitting-field statement).

🤖 Prepared with Claude Code

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
@kim-em kim-em merged commit 1f184b9 into main May 1, 2026
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@kim-em kim-em deleted the add-cfsg-and-brauer-problems branch May 1, 2026 08:06
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