Greedy base sizes for sporadic simple groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917758947557376 |
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| author | del Valle, Coen |
| author_facet | del Valle, Coen |
| contents | A base for a permutation group $G$ acting on a set $Ω$ is a sequence $\mathcal{B}$ of points of $Ω$ such that the pointwise stabiliser $G_{\mathcal{B}}$ is trivial. Denote the minimum size of a base for $G$ by $b(G)$. There is a natural greedy algorithm for constructing a base of relatively small size; denote by $\mathcal{G}(G)$ the maximum size of a base it produces. Motivated by a long-standing conjecture of Cameron, we determine $\mathcal{G}(G)$ for every almost simple primitive group $G$ with socle a sporadic simple group, showing that $\mathcal{G}(G)=b(G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Greedy base sizes for sporadic simple groups del Valle, Coen Group Theory A base for a permutation group $G$ acting on a set $Ω$ is a sequence $\mathcal{B}$ of points of $Ω$ such that the pointwise stabiliser $G_{\mathcal{B}}$ is trivial. Denote the minimum size of a base for $G$ by $b(G)$. There is a natural greedy algorithm for constructing a base of relatively small size; denote by $\mathcal{G}(G)$ the maximum size of a base it produces. Motivated by a long-standing conjecture of Cameron, we determine $\mathcal{G}(G)$ for every almost simple primitive group $G$ with socle a sporadic simple group, showing that $\mathcal{G}(G)=b(G)$. |
| title | Greedy base sizes for sporadic simple groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2408.14139 |