Alphabeta MathHow 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.
Indecomposable and decomposable nontrivial finite abelian groups
Definition
A nontrivial finite abelian group is indecomposable if it is not an internal direct product of two nontrivial subgroups in the sense of Internal direct products of finitely many normal subgroups. It is decomposable if such a product exists. The trivial group is assigned neither label.
Depends on
Used by
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 8 results over 5 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
- Keith Conrad, Decomposition of Finite Abelian Groups, §§1-4 (standard reference, not scraped)
- Richard Elman, Lectures on Abstract Algebra, Ch. 14 (standard reference, not scraped)