Integer Group Determinants for All Groups of Order 20
Year: 2026
Type: preprint
Abstract: We determine the integer group-determinant spectra of C20, C2 × C10, and thedicyclic group Q20. For C20, two exceptional valuation faces arecharacterized by prime-power divisibility conditions and explicit quadraticcharacters at split primes. For C2 × C10, we give a complete sixteen-statecriterion that retains all conductor compatibility conditions and thedependence on sign. For Q20, we resolve the remaining valuation-five face bythree uniform prime-power families. The proofs use integral normalizationpullbacks, complete unit images, ray-character comparisons, and a quaternionideal class calculation; the required finite computations have exactreproducible certificates. We also give a self-contained correctedspecialization for GA(1,5). Combining these results with Boerkoel–Pinner'sdihedral theorem completes the integer group-determinant classification forall five groups of order 20.
Author: Radolović, Alen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7210275751