{
  "abstract": "We determine the integer group determinant sets for $C_{24}$, $C_2\\times C_{12}$ and $C_2^2\\times C_6$, the three abelian groups of order $24$. Character factorization expresses each determinant as a product of cyclotomic norms, whose components must satisfy integral compatibility conditions. The classifications are constructive and reduce each nonzero signed integer to valuation conditions at $2$ and $3$ and a finite test on its remaining prime factors. The tests use conductor quotients and norm-preserving global units. Each prime contribution has a uniform bound independent of its multiplicity, and successful tests yield integer coefficients realizing the prescribed determinant. The critical cyclic strata share one compatibility group. For $C_2^2\\times C_6$, a normalized rational--Eisenstein pair settles the odd values and most even strata; target stabilizers reduce the remaining tests. We also prove that the odd determinant set of $C_2^2\\times C_6$ is properly contained in that of $C_2\\times C_{12}$, exhibit an infinite family in the difference, and determine the signed powers of two in all three sets. Exact arithmetic certificates and coefficient constructors accompany the proofs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10423",
  "author_total": 1,
  "authors": [
    {
      "name": "Chatchawan Panraksa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/71n0je5p7tshw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10423",
  "fulltext_url": null,
  "id": "71n0je5p7tshw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10423",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7212144969",
  "pdf_url": "https://arxiv.org/pdf/2609.10423",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/71n0je5p7tshw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:16Z",
      "native_id": "2609.10423",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10423"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Integer group determinants for abelian groups of order 24",
  "title_text": "Integer group determinants for abelian groups of order 24",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:16Z",
  "url": "https://research.draconitic.com/paper/71n0je5p7tshw",
  "venue": "arXiv",
  "versions": []
}