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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/2510.23759 |
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| _version_ | 1866909873156915200 |
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| author | Estanislau, Marlon |
| author_facet | Estanislau, Marlon |
| contents | Let $G$ be a cyclic $p$-group for some prime number $p>0$ and let $R$ be a complete discrete valuation ring in mixed characteristic. In this paper, we present a generalization of two results that characterize $RG$-permutation modules, extending previous work by B. Torrecillas and Th. Weigel. Their original results were established under the assumption that $ p$ is unramified in $R$, whereas we extend their characterization to the case where $p$ may be ramified. Unlike prior approaches, our proofs rely solely on fundamental facts from group cohomology and a version of Weiss' Theorem, avoiding deeper categorical techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Permutation modules over cyclic $p$-groups Estanislau, Marlon Representation Theory 20c11 Let $G$ be a cyclic $p$-group for some prime number $p>0$ and let $R$ be a complete discrete valuation ring in mixed characteristic. In this paper, we present a generalization of two results that characterize $RG$-permutation modules, extending previous work by B. Torrecillas and Th. Weigel. Their original results were established under the assumption that $ p$ is unramified in $R$, whereas we extend their characterization to the case where $p$ may be ramified. Unlike prior approaches, our proofs rely solely on fundamental facts from group cohomology and a version of Weiss' Theorem, avoiding deeper categorical techniques. |
| title | Permutation modules over cyclic $p$-groups |
| topic | Representation Theory 20c11 |
| url | https://arxiv.org/abs/2510.23759 |