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arXiv · 2602.04111

Multiplicative Subgroups of $\mathbb{Z}_p^*$ that are Generalized Arithmetic Progressions

Albert Cochrane
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Abstract

We prove that a multiplicative subgroup $A_k$ of $\mathbb{Z}_p^*$ is a generalized arithmetic progression if and only if $|A_k| = 2,\ 4,$ or $p-1$. Much of the argument is built upon recent work studying additive decompositions of subgroups of $\mathbb{Z}_p^*$, and we generalize a result of Hanson and Petridis to show that any additive $n$-decomposition of a subgroup must be a direct sum.

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BibTeXRIS

Albert Cochrane. 2026-02-04. Multiplicative Subgroups of $\mathbb{Z}_p^*$ that are Generalized Arithmetic Progressions. https://arxiv.org/abs/2602.04111

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