The automorphism groups of small affine rank 3 graphs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914829292273664 |
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| author | Guo, Jin Vasil'ev, Andrey V. Wang, Rui |
| author_facet | Guo, Jin Vasil'ev, Andrey V. Wang, Rui |
| contents | A rank 3 graph is an orbital graph of a rank 3 permutation group of even order. Despite the classification of rank 3 graphs being complete, see, e.g., Chapter 11 of the recent monograph 'Strongly regular graphs' by Brouwer and Van Maldeghem, the full automorphism groups of these graphs (equivalently, the 2-closures of rank 3 groups) have not been explicitly described, though a lot of information on this subject is available. In the present note, we address this problem for the affine rank 3 graphs. We find the automorphism groups for finitely many relatively small graphs and show that modulo known results, this provides the full description of the automorphism groups of the affine rank 3 graphs, thus reducing the general problem to the case when the socle of the automorphism group is nonabelian simple. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_04559 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The automorphism groups of small affine rank 3 graphs Guo, Jin Vasil'ev, Andrey V. Wang, Rui Combinatorics Group Theory 20B25, 05E18, 05E30 A rank 3 graph is an orbital graph of a rank 3 permutation group of even order. Despite the classification of rank 3 graphs being complete, see, e.g., Chapter 11 of the recent monograph 'Strongly regular graphs' by Brouwer and Van Maldeghem, the full automorphism groups of these graphs (equivalently, the 2-closures of rank 3 groups) have not been explicitly described, though a lot of information on this subject is available. In the present note, we address this problem for the affine rank 3 graphs. We find the automorphism groups for finitely many relatively small graphs and show that modulo known results, this provides the full description of the automorphism groups of the affine rank 3 graphs, thus reducing the general problem to the case when the socle of the automorphism group is nonabelian simple. |
| title | The automorphism groups of small affine rank 3 graphs |
| topic | Combinatorics Group Theory 20B25, 05E18, 05E30 |
| url | https://arxiv.org/abs/2406.04559 |