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arXiv · 2510.20418

On cohomologically Trivially modules over finite $p$-groups

Yassine Guerboussa·Maria Guedri
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Abstract

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.

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Yassine Guerboussa, Maria Guedri. 2025-10-23. On cohomologically Trivially modules over finite $p$-groups. https://arxiv.org/abs/2510.20418

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