发表机构
Mahidol University International College（玛希隆大学国际学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过特征分解和有限检验，确定了三个24阶阿贝尔群的整数群行列式集合，并证明了奇行列式集合的包含关系及无限族差异。
AI 中文摘要
我们确定了$C_{24}$、$C_2\ imes C_{12}$和$C_2^2\ imes C_6$这三个24阶阿贝尔群的整数群行列式集合。特征分解将每个行列式表示为分圆范数的乘积，其分量必须满足积分相容性条件。分类是构造性的，将每个非零带符号整数归结为在2和3处的赋值条件以及对其剩余素因子的有限检验。检验使用导子商和保范全局单位。每个素数贡献有一个与其重数无关的一致上界，成功的检验产生实现指定行列式的整数系数。关键循环层共享一个相容性群。对于$C_2^2\ imes C_6$，一个规范化的有理-艾森斯坦对解决了奇数值和大多数偶层；目标稳定子减少了剩余检验。我们还证明了$C_2^2\ imes C_6$的奇行列式集合真包含于$C_2\ imes C_{12}$的奇行列式集合中，展示了差集中的无限族，并确定了所有三个集合中2的带符号幂。精确算术证书和系数构造器伴随证明给出。
英文摘要
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.
Comments30 pages, 0 figures. Code and certificates: https://github.com/chatchawanpan-dev/order24-group-determinants/releases/tag/v1.0.0
