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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.11469 |
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| _version_ | 1866915391218909184 |
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| author | Harman, Henry |
| author_facet | Harman, Henry |
| contents | Let $G$ be a finite group and $k$ a field of characteristic $p > 0$. Balmer and Gallauer's recent result on finite $p$-permutation resolutions of $kG$-modules motivates the study of an intriguing new invariant; the $p$-permutation dimension. Following Walsh's success with cyclic groups of prime order, we compute the (global) $p$-permutation dimension of the Klein 4-group in characteristic $p := 2$, along with the dimensions for each of its indecomposable modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11469 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The permutation dimension of the Klein 4-group Harman, Henry Representation Theory 20C20 Let $G$ be a finite group and $k$ a field of characteristic $p > 0$. Balmer and Gallauer's recent result on finite $p$-permutation resolutions of $kG$-modules motivates the study of an intriguing new invariant; the $p$-permutation dimension. Following Walsh's success with cyclic groups of prime order, we compute the (global) $p$-permutation dimension of the Klein 4-group in characteristic $p := 2$, along with the dimensions for each of its indecomposable modules. |
| title | The permutation dimension of the Klein 4-group |
| topic | Representation Theory 20C20 |
| url | https://arxiv.org/abs/2507.11469 |