DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)audited 2026-08-13

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.

Simple groups

Definition

A group $G$ is simple if $G \neq {1}$ and its only normal subgroups are ${1}$ and $G$ , where normality is as in Normal subgroup: invariance under conjugation.

Depends on

Normal subgroup: invariance under conjugation

Used by

FALSE: Aₙ is simple for every n≥4 False statement
Aₙ is simple for every n≥5 Theorem

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 7 results over 7 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

T. Judson, Abstract Algebra: Theory and Applications, Simplicity of $A_n$ (standard reference, not scraped)