Integer Group Determinants for C₂ × C₁₀: A Complete Sixteen-State Classification
Alen Radolović · Zenodo (CERN European Organization for Nuclear Research) · 2026
Let G = C₂ × C₁₀ ≅ C₂² × C₅. This preprint gives a complete effective classification of the integer values of its group determinant. An exact normalization pullback reduces the remaining compatibility conditions to a fixed sixteen-state group C₂⁴. Explicit Frobenius packets classify primes coprime to 10, while complete signed tables treat the 2- and 5-primary faces. The resulting criterion is necessary and sufficient, includes exact pure prime-power spectra and noncongruential split-prime phenomena, and is accompanied by independently reproducible verification programs.