Source labels openChecked July 26, 2026

Babai–Seress Conjectures on the Diameter of Finite Groups

Babai–Seress Conjecture (Conjecture 1.5)**: There exists an absolute constant $C$ such that the diameter of the alternating group $A_n$ satisfies $\operatorname{diam}(A_n) \leq n^C.$ Reference: [L. Babai and Á. Seress, *On the diameter of permutation gr...

Combinatorics AMS 5 AMS 20 AMS 68

Mathematical statement

Babai–Seress Conjecture (Conjecture 1.5)**: There exists an absolute constant $C$ such that the diameter of the alternating group $A_n$ satisfies $\operatorname{diam}(A_n) \leq n^C.$ Reference: L. Babai and Á. Seress, On the diameter of permutation groups, European Journal of Combinatorics 13 (1992), Conjecture 1.5

Statement source: Wikipedia 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

babai_seress_conjecture_alternating

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem babai_seress_conjecture_alternating :    ∃ C : ℕ, ∀ n : ℕ,    (groupDiam (alternatingGroup (Fin n)) : ℝ) ≤ (n : ℝ) ^ C := 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 L. Babai and Á. Seress, *On the diameter of permutation groups*, European Journal of Combinatorics 13 (1992), Conjecture 1.5background Wikipedia, *Diameter (group theory)*background H. A. Helfgott and Á. Seress, *On the diameter of permutation groups*background