On the base size and minimal degree of transitive groups
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908415895273472 |
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| author | Guerra, Lorenzo Maróti, Attila Mastrogiacomo, Fabio Spiga, Pablo |
| author_facet | Guerra, Lorenzo Maróti, Attila Mastrogiacomo, Fabio Spiga, Pablo |
| contents | Let $G$ be a permutation group, and denote with $μ(G)$ and $b(G)$ its minimal degree and base size respectively. We show that for every $\varepsilon>0$, there exists a transitive permutation group $G$ of degree $n$ with \[
μ(G)b(G) \geq n^{2-\varepsilon}. \] We also identify some classes of transitive and intransitive groups whose base size and minimal degree have a smaller upper bound, shared with primitive groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17668 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the base size and minimal degree of transitive groups Guerra, Lorenzo Maróti, Attila Mastrogiacomo, Fabio Spiga, Pablo Group Theory Let $G$ be a permutation group, and denote with $μ(G)$ and $b(G)$ its minimal degree and base size respectively. We show that for every $\varepsilon>0$, there exists a transitive permutation group $G$ of degree $n$ with \[ μ(G)b(G) \geq n^{2-\varepsilon}. \] We also identify some classes of transitive and intransitive groups whose base size and minimal degree have a smaller upper bound, shared with primitive groups. |
| title | On the base size and minimal degree of transitive groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2506.17668 |