DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 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.

Group isomorphisms, automorphisms and the set $Aut (G)$

Definition

Group isomorphisms, automorphisms and the set $Aut (G)$ .

An isomorphism $f : G \to H$ is a bijective group homomorphism (Monoid homomorphism and group homomorphism, Injection, surjection, bijection). When $G = H$ , it is an automorphism of $G$ . Write

$Aut (G) : = {f : G \to G : f is an automorphism} .$

Depends on

Dependency tree · 2 levels

Sources

Judson, Abstract Algebra: Theory and Applications, Isomorphism Theorems