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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.19710 |
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Table of Contents:
- Let $G$ be a finite $p$-group with normal subgroup $N$, and $R$ a complete discrete valuation ring in mixed characteristic. We characterize permutation $RG$-modules in terms of modules for $RN$ and $R[G/N]$. The result generalizes both the seminal detection theorem for permutation modules due to Weiss, who characterizes those permutation $RG$-modules that are $RN$-free when $R$ is a finite extension of $\mathbb{Z}_p$, and a more recent result of MacQuarrie and Zalesskii, who prove a characterization of permutation modules when $N$ has order $p$ and $R = \mathbb{Z}_p$.