DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 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.

Principal crossed homomorphism for abelian coefficients

Definition

Let $G$ act on an abelian group $A$ . For $a \in A$ , the map

$d a : G \to A, (d a) (g) = g \cdot a - a,$

is the principal crossed homomorphism determined by $a$ .

The set of all such maps is denoted $B^{1} (G, A)$ .

Depends on

Crossed homomorphism for a G-group

Used by

Dependency tree · two levels

2 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

David A. Craven, Finite Group Theory (standard reference, not scraped)