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 centre of an extraspecial -group has a complement
Statement refuted
the centre of an extraspecial -group has a complement.
Facts & Assumptions
Given: The proposed claim together with the witness named in the Statement refuted.
The centre of an extraspecial -group has no complement (The centre of an extraspecial -group has no complement).
In this situation is called a complement to in . (An internal semidirect product and a complement to a normal subgroup).
Refutation
The claim asserts the existence of a subgroup meeting the centre trivially and multiplying with it to the whole group.
Such a subgroup would be isomorphic to the elementary abelian central quotient, hence abelian, forcing the whole group to be abelian.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
10 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
- D. A. Craven, The Theory of p-Groups (Hilary Term 2008), 48 pp. (standard reference, not scraped)
- M. van Beek, Topics in Finite p-Groups, 62 pp. (standard reference, not scraped)
- D. Kaur and A. Kulshrestha, Characters of real special 2-groups (arXiv:1510.06583v1) (standard reference, not scraped)