The $(2,3)$-generation of the finite simple odd-dimensional orthogonal groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916092933308416 |
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| author | Pellegrini, M. A. Bellani, M. C. Tamburini |
| author_facet | Pellegrini, M. A. Bellani, M. C. Tamburini |
| contents | The complete classification of the finite simple groups that are $(2,3)$-generated is a problem which is still open only for orthogonal groups. Here, we construct $(2, 3)$-generators for the finite odd-dimensional orthogonal groups $Ω_{2k+1}(q)$, $k\geq 4$. As a byproduct we also obtain $(2,3)$-generators for $Ω_{4k}^+(q)$ with $k\geq 3$ and $q$ odd, and for $Ω_{4k+2}^\pm(q)$ with $k\geq 4$ and $q\equiv \pm 1 \pmod 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_02390 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The $(2,3)$-generation of the finite simple odd-dimensional orthogonal groups Pellegrini, M. A. Bellani, M. C. Tamburini Group Theory 20G40 The complete classification of the finite simple groups that are $(2,3)$-generated is a problem which is still open only for orthogonal groups. Here, we construct $(2, 3)$-generators for the finite odd-dimensional orthogonal groups $Ω_{2k+1}(q)$, $k\geq 4$. As a byproduct we also obtain $(2,3)$-generators for $Ω_{4k}^+(q)$ with $k\geq 3$ and $q$ odd, and for $Ω_{4k+2}^\pm(q)$ with $k\geq 4$ and $q\equiv \pm 1 \pmod 4$. |
| title | The $(2,3)$-generation of the finite simple odd-dimensional orthogonal groups |
| topic | Group Theory 20G40 |
| url | https://arxiv.org/abs/2306.02390 |