Alphabeta Math
DefinitionDefinition: AI-adaptedProof: Not applicableSession-authored (Fable 5 assisted)audited 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 GG, its exponent is exp⁡(G)=min⁡{n∈N:n>0 and gn=e for every g∈G}.\exp(G)=\min\{n\in\mathbb N:n>0\text{ and }g^n=e\text{ for every }g\in G\}. The set is nonempty by g∣G∣=eg^{|G|}=e for every element gg of a finite group GG, and The well-ordering principle gives its least member; powers use Powers gng^{n}: natural exponents in a monoid and integer exponents in a group, with g0=eg^{0} = e. Thus the definition is well-defined. For the trivial group exp⁡(G)=1\exp(G)=1.

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 61 results over 19 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources