The $S_3$-conjecture (conjugacy classes of distinct sizes)
Markel's -conjecture* (1973): any nontrivial finite ah-group is isomorphic to .
Mathematical statement
Markel's -conjecture* (1973): any nontrivial finite ah-group is isomorphic to .
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
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