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arXiv · 2609.21224

The integer group determinants for $\mathbb{Z}_p^n$

Michael J. Mossinghoff·Christopher Pinner
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Abstract

We give new conditions on allowable powers of a prime $p$ dividing an integer group determinant for the group $\mathbb{Z}_p^n$, and show these conditions are sharp for $n\leq 5$. The values coprime to $p$ for these groups are already known; determining which multiples of allowable powers of $p$ occur is much more complicated. We show that all multiples of sufficiently large powers of $p$ occur as integer group determinants of $\mathbb{Z}_p^n$. We also provide a complete characterization for the group $\mathbb{Z}_3^3$, where particular arithmetic conditions are required for multiples of certain powers of $3$.

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Michael J. Mossinghoff, Christopher Pinner. 2026-09-18. The integer group determinants for $\mathbb{Z}_p^n$. https://arxiv.org/abs/2609.21224

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