The binary actions of simple groups with a single conjugacy class of involutions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914666178936832 |
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| author | Gill, Nick Guillot, Pierre |
| author_facet | Gill, Nick Guillot, Pierre |
| contents | We continue our investigation of binary actions of simple groups. In this paper, we demonstrate a connection between the graph $Γ(\mathcal{C})$ based on the conjugacy class $\mathcal{C}$ of the group $G$, which was introduced in our previous work, and the notion of a strongly embedded subgroup of $G$. We exploit this connection to prove a result concerning the binary actions of finite simple groups that contain a single conjugacy class of involutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02269 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The binary actions of simple groups with a single conjugacy class of involutions Gill, Nick Guillot, Pierre Group Theory We continue our investigation of binary actions of simple groups. In this paper, we demonstrate a connection between the graph $Γ(\mathcal{C})$ based on the conjugacy class $\mathcal{C}$ of the group $G$, which was introduced in our previous work, and the notion of a strongly embedded subgroup of $G$. We exploit this connection to prove a result concerning the binary actions of finite simple groups that contain a single conjugacy class of involutions. |
| title | The binary actions of simple groups with a single conjugacy class of involutions |
| topic | Group Theory |
| url | https://arxiv.org/abs/2402.02269 |