DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-04

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.

Complete group

Definition

A group $N$ is complete when both of the following hold:

its center is trivial, $Z (N) = 1$ (The center $Z (G)$ of a group);
its outer automorphism group is trivial, $Out (N) = 1$ ( The outer automorphism group $Out (G) = Aut (G) / Inn (G)$ ).

Equivalently, every automorphism of $N$ is inner and no nontrivial element of $N$ commutes with all of $N$ .

Depends on

Used by

If the kernel is complete, the extension splits over its centralizer Proposition

Dependency tree · two levels

6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

J. S. Milne, Group Theory (standard reference, not scraped)