exactly two groups of order p² (from order-p²-abelian)
Theorem.exactly two groups of order p² (from order-p²-abelian) — #Grp(p²) = 2 — ℤ_{p²} and ℤ_p × ℤ_p.
Proof.both abelian (wave 48), so Z_{p²} and Z_p×Z_p, distinguished by an order-p² element — verified non-isomorphic for p = 3: THIRD-order compounding.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveFortyNine
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"exactly two groups of order p² (from order-p²-abelian)" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation discoveredTheoremsWaveFortyNine.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (discoveredTheoremsWaveFortyNine @ src/9/1) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes discoveredTheoremsWaveFortyNine (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.