Low rank groups of Lie type acting point and line-primitively on finite generalised quadrangles
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910844481175552 |
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| author | Arumugam, Vishnuram Bamberg, John Giudici, Michael |
| author_facet | Arumugam, Vishnuram Bamberg, John Giudici, Michael |
| contents | Suppose we have a finite thick generalised quadrangle whose automorphism group $G$ acts primitively on both the set of points and the set of lines. Then $G$ must be almost simple. In this paper, we show that $\operatorname{soc}(G)$ cannot be isomorphic to $\operatorname{Sz}(2^{2m+1})$ or $\operatorname{Ree}(3^{2m+1})$ where $m$ is a positive integer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03790 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Low rank groups of Lie type acting point and line-primitively on finite generalised quadrangles Arumugam, Vishnuram Bamberg, John Giudici, Michael Group Theory 51E12 (Primary), 20B25 (Secondary) Suppose we have a finite thick generalised quadrangle whose automorphism group $G$ acts primitively on both the set of points and the set of lines. Then $G$ must be almost simple. In this paper, we show that $\operatorname{soc}(G)$ cannot be isomorphic to $\operatorname{Sz}(2^{2m+1})$ or $\operatorname{Ree}(3^{2m+1})$ where $m$ is a positive integer. |
| title | Low rank groups of Lie type acting point and line-primitively on finite generalised quadrangles |
| topic | Group Theory 51E12 (Primary), 20B25 (Secondary) |
| url | https://arxiv.org/abs/2405.03790 |