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.
FALSE: the O'Nan-Scott theorem is the classification of finite simple groups
Statement
False claim: the O'Nan-Scott theorem is the classification of finite simple groups.
Facts & Assumptions
Given: The finite O'Nan-Scott theorem and the classification of finite simple groups are distinct named results.
The O'Nan-Scott theorem classifies finite primitive permutation groups of degree at least by socle type (The O'Nan-Scott classification of finite primitive groups).
Later refinements involving finite simple groups lie beyond the structural O'Nan-Scott reduction.
Refutation
By [L1], the O'Nan-Scott theorem concerns primitive permutation actions, not the class of all finite simple groups.
The sourced boundary fact [A1] separates the structural reduction from the later theory of finite simple groups. Therefore the two theorems serve different purposes, and the claim is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
8 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
- Leonard H. Soicher, Primitive permutation groups (standard reference, not scraped)