On the orbital diameter of classical groups in standard action
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915758846509056 |
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| author | Maróti, Attila Rekvényi, Kamilla |
| author_facet | Maróti, Attila Rekvényi, Kamilla |
| contents | Let $G$ be a primitive permutation group acting on a finite set $X$. The orbital diameter $\mathrm{diam}(X,G)$ is defined to be the supremum of the diameters of the (connected) orbital graphs of $G$ after disregarding the directions of all edges in the graphs. This invariant is studied in the case when $G$ is an almost simple group in a standard action. A lower bound is given for $\mathrm{diam}(X,G)$ and we provide a partial classification of pairs $(X,G)$ for which the orbital diameter is at most $2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20508 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the orbital diameter of classical groups in standard action Maróti, Attila Rekvényi, Kamilla Group Theory Combinatorics Let $G$ be a primitive permutation group acting on a finite set $X$. The orbital diameter $\mathrm{diam}(X,G)$ is defined to be the supremum of the diameters of the (connected) orbital graphs of $G$ after disregarding the directions of all edges in the graphs. This invariant is studied in the case when $G$ is an almost simple group in a standard action. A lower bound is given for $\mathrm{diam}(X,G)$ and we provide a partial classification of pairs $(X,G)$ for which the orbital diameter is at most $2$. |
| title | On the orbital diameter of classical groups in standard action |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2601.20508 |