DefinitionDefinition: AI-adaptedProof: Not applicableaudited 2026-08-11

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

The exponent of a finite group

Definition

For a finite group $G$ , its exponent is $\exp (G) = \min {n \in N : n > 0 and g^{n} = e for every g \in G} .$ The set is nonempty by $g^{∣ G ∣} = e$ for every element $g$ of a finite group $G$ , and The well-ordering principle gives its least member; powers use Powers $g^{n}$ : natural exponents in a monoid and integer exponents in a group, with $g^{0} = e$ . Thus the definition is well-defined. For the trivial group $\exp (G) = 1$ .

Depends on

Dependency tree · 2 levels

Sources