On cohomologically Trivially modules over finite $p$-groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918167250468864 |
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| author | Guerboussa, Yassine Guedri, Maria |
| author_facet | Guerboussa, Yassine Guedri, Maria |
| contents | We show that every finitely generated cohomologically trivial module over $RG$, where $G$ is a finite $p$-group and $R$ is a $p$-adic ring, splits as the direct sum of a finite cohomologically trivial $RG$-module and a free $RG$-module. Along the way, we also establish other results concerning generators and relators of such modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20418 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On cohomologically Trivially modules over finite $p$-groups Guerboussa, Yassine Guedri, Maria Group Theory 20J06, 20D15 We show that every finitely generated cohomologically trivial module over $RG$, where $G$ is a finite $p$-group and $R$ is a $p$-adic ring, splits as the direct sum of a finite cohomologically trivial $RG$-module and a free $RG$-module. Along the way, we also establish other results concerning generators and relators of such modules. |
| title | On cohomologically Trivially modules over finite $p$-groups |
| topic | Group Theory 20J06, 20D15 |
| url | https://arxiv.org/abs/2510.20418 |