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.
Conventions and proved scope for free products and amalgamation
Remark
Free products here allow arbitrary index sets, and group pushouts allow arbitrary homomorphisms. The notation is reserved for injective maps from ; only in that setting do the normal-form, factor-embedding, and intersection theorems apply. The kernel-collapse proposition explains why those conclusions fail for general pushouts. HNN extensions, Kurosh and Grushko theorems, and Bass-Serre theory require machinery outside this development's declared prerequisites.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 40 results over 13 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
- George D. Torres, Combinatorial Group Theory, §2 (standard reference, not scraped)
- B. H. Neumann, Lectures on Topics in the Theory of Infinite Groups, Ch. 9 (standard reference, not scraped)