All open problems
Source labels openChecked July 26, 2026
Green's Open ProblemsGroup theory
Ben Green's Open Problem 4
What is the largest product-free set in the alternating group ?
Mathematical statement
What is the largest product-free set in the alternating group ?
Statement source: Green's Open Problems 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
green_4
Complete statement target, proof intentionally absentLean 4
theorem green_4 (n : ℕ) : let S : ∀ n, Set (alternatingGroup <| Fin n) := answer(sorry) MaximalFor (ProdFree (M := alternatingGroup <| Fin n)) Set.ncard (S n) := 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