DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)audited 2026-08-02

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.

Inner automorphisms and $\operatorname{Inn}(G)$

Definition

Inner automorphisms and $\operatorname{Inn}(G)$ .

For $g\in G$ , write $c_g(x)=gxg^{-1}$ . By Conjugation $x\mapsto gxg^{-1}$ is an automorphism, $c_g\in\operatorname{Aut}(G)$ . Define

$\operatorname{Inn}(G):=\{c_g:g\in G\}\subseteq\operatorname{Aut}(G).$

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 16 results over 10 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

Milne, Group Theory, Automorphisms of Groups (standard reference, not scraped)

Inner automorphisms and Inn⁡(G)\operatorname{Inn}(G)Inn(G)