On $\operatorname{Alt}(n)$-modules with an additive dimension when $n\le6$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917348986847232 |
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| author | Chin, Barry Deloro, Adrien Wiscons, Joshua Yu, Andy |
| author_facet | Chin, Barry Deloro, Adrien Wiscons, Joshua Yu, Andy |
| contents | Working in the general context of "modules with an additive dimension," we complete the determination of the minimal dimension of a faithful Alt(n)-module and classify those modules in three of the exceptional cases: 2-dimensional Alt(5)-modules in characteristic 2, 3-dimensional Alt(5)-modules in characteristic 5, and 3-dimensional Alt(6)-modules in characteristic 3. We also highlight the remaining work needed to complete the classification of the faithful Alt(n)-modules of minimal dimension for all n; these open problems seem well suited as projects for advanced undergraduate or master's students. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_05230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $\operatorname{Alt}(n)$-modules with an additive dimension when $n\le6$ Chin, Barry Deloro, Adrien Wiscons, Joshua Yu, Andy Group Theory Logic Primary 20C30, Secondary 03C60, 20F11 Working in the general context of "modules with an additive dimension," we complete the determination of the minimal dimension of a faithful Alt(n)-module and classify those modules in three of the exceptional cases: 2-dimensional Alt(5)-modules in characteristic 2, 3-dimensional Alt(5)-modules in characteristic 5, and 3-dimensional Alt(6)-modules in characteristic 3. We also highlight the remaining work needed to complete the classification of the faithful Alt(n)-modules of minimal dimension for all n; these open problems seem well suited as projects for advanced undergraduate or master's students. |
| title | On $\operatorname{Alt}(n)$-modules with an additive dimension when $n\le6$ |
| topic | Group Theory Logic Primary 20C30, Secondary 03C60, 20F11 |
| url | https://arxiv.org/abs/2405.05230 |