Source labels openChecked July 26, 2026

Ben Green's Open Problem 5: Sl Two

A good model problem would be to determine the largest product-free subsets of $\mathrm{SL}_2(\mathbb{F}_p)$ .

Combinatorics AMS 5 AMS 20

Mathematical statement

A good model problem would be to determine the largest product-free subsets of $\mathrm{SL}_2(\mathbb{F}_p)$ .

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_5.variants.sl_two

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_5.variants.sl_two (p : ℕ) [Fact p.Prime] :    let S : Finset (SL₂ p) := answer(sorry)    MaximalFor (IsProductFree (M := SL₂ p)) Set.ncard (S : Set (SL₂ p)) := 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

Pinned Formal Conjectures sourceformalization Green, Ben. "100 open problems." (2024).background