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Source labels openChecked July 26, 2026

PapersGroup theory

The $S_3$-conjecture (conjugacy classes of distinct sizes)

Markel's S3S_3-conjecture* (1973): any nontrivial finite ah-group is isomorphic to S3S_3.

Mathematical statement

Markel's S3S_3-conjecture* (1973): any nontrivial finite ah-group is isomorphic to S3S_3.

The conjecture is open in general; it is known to be true for solvable groups.

Statement source: Papers statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

conjClassSizes_iff_sym_three

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem conjClassSizes_iff_sym_three    (G : Type) [Group G] [Fintype G] [Nontrivial G]    (h : HasDistinctConjClassSizes (G := G)) :    Nonempty (G ≃* Equiv.Perm (Fin 3)) := by  sorry
Statement source
Formal Conjectures
Lean version
v4.27.0
Placeholder
Present; no proof artifact
Source evidence
Pinned source index
Fidelity review
Community formulation

References