Components and realizability of fusion systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911085174456320 |
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| author | Henke, Ellen Lynd, Justin |
| author_facet | Henke, Ellen Lynd, Justin |
| contents | For $p\in\{2,3\}$ it is known that a saturated $p$-fusion system is realizable if and only if each of its components is realizable by a finite simple group. For primes $p\geq 5$ this is false. Building on work of Broto, Møller, Oliver and Ruiz, we show however that a fusion system $\mathcal{F}$ is realizable if and only if for each of its components $\mathcal{C}$ there exists a realizable subnormal subsystem $\mathcal{E}$ of $\mathcal{F}$ with $O^{p^\prime}(\mathcal{E})=\mathcal{C}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_19826 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Components and realizability of fusion systems Henke, Ellen Lynd, Justin Group Theory 20D05, 20E25, 20D20, 20D35 For $p\in\{2,3\}$ it is known that a saturated $p$-fusion system is realizable if and only if each of its components is realizable by a finite simple group. For primes $p\geq 5$ this is false. Building on work of Broto, Møller, Oliver and Ruiz, we show however that a fusion system $\mathcal{F}$ is realizable if and only if for each of its components $\mathcal{C}$ there exists a realizable subnormal subsystem $\mathcal{E}$ of $\mathcal{F}$ with $O^{p^\prime}(\mathcal{E})=\mathcal{C}$. |
| title | Components and realizability of fusion systems |
| topic | Group Theory 20D05, 20E25, 20D20, 20D35 |
| url | https://arxiv.org/abs/2504.19826 |