Alphabeta Math
RemarkRemark: Literature-sourcedProof: Not suppliedaudited 2026-09-04‡ sources checked 2026-09-04‡ not proved here
How 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.

‡ Recorded, not proved here. This statement is included so the library can refer to it honestly, with a citation to the literature. It is not proved anywhere in this library: the track that would prove it has not been developed here yet.

The full Schur-Zassenhaus conjugacy theorem

Remark

The clean modern statement of Schur-Zassenhaus says: if N⊴G is a normal Hall subgroup of a finite group, then complements to N exist and any two of them are conjugate in G.

This page proves that conjugacy statement only under the classical solvability hypothesis on the kernel or quotient. Craven's full formulation explains that the remaining solvability-free reduction uses deeper finite-group input, so the stronger statement is recorded here but not proved locally.

Depends on

Used by

Dependency tree · two levels

7 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