Babai–Seress Conjectures on the Diameter of Finite Groups

formal-conjectures · wikipedia · ams-5 · ams-20 · ams-68

**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](https://doi.org/10.1016/S0195-6698(05)80029-0)

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://en.wikipedia.org/wiki/Diameter_
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://arxiv.org/abs/1109.3550
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://doi.org/10.1016/S0195-6698
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/DiameterSimpleFiniteGroups.lean
Local target: Corpus.WikipediaDiameterSimpleFiniteGroups.babai_seress_conjecture_alternating
Source SHA-256: e250a92523a9cc6ee74b794c339573dc1f762c92c88fbcfb743c1194d5769556
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record