Source labels openChecked July 26, 2026

Bounded Burnside problem

Let $G$ be a finitely generated group, and assume there exists $n$ such that for every $g$ in $G$ , $g^n = 1$ . Is $G$ necessarily finite?

Group theory AMS 20

Mathematical statement

Let $G$ be a finitely generated group, and assume there exists $n$ such that for every $g$ in $G$ , $g^n = 1$ . Is $G$ necessarily finite?

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

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

bounded_burnside_problem

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem bounded_burnside_problem :    answer(sorry) ↔ ∀ (G : Type) [Group G] (fin_gen : Group.FG G)      (n : ℕ) (hn : n > 0) (bounded : ∀ g : G, g^n = 1), Finite G := 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 Wikipediabackground