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.
The vertex of an indecomposable module is literally a graph vertex of a Cayley graph
Statement
The vertex of an indecomposable module is literally a graph vertex of a Cayley graph.
Facts & Assumptions
Given: An indecomposable -module.
A vertex is a minimal -subgroup for relative projectivity (A vertex is a minimal p-subgroup for relative projectivity, and a source is an indecomposable inducing summand there).
Refutation
By [F1], a module vertex is a subgroup of , not a point in a graph.
The shared word "vertex" is only terminology. A Cayley-graph vertex is a group element, whereas the representation-theoretic vertex is a -subgroup defined by relative projectivity. Therefore the statement is false.
So the claimed literal identification fails.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
3 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
- J. MacQuarrie, Modular Representations of Profinite Groups (standard reference, not scraped)