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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.04111 |
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Table of Contents:
- 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.