Bounding $s$ for vertex-primitive $s$-arc-transitive digraphs of alternating and symmetric groups
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866909116017934336 |
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| author | Chen, Junyan Chen, Lei Giudici, Michael Li, Jing Jian Praeger, Cheryl E. Xia, Binzhou |
| author_facet | Chen, Junyan Chen, Lei Giudici, Michael Li, Jing Jian Praeger, Cheryl E. Xia, Binzhou |
| contents | Determining an upper bound on $s$ for finite vertex-primitive $s$-arc-transitive digraphs has received considerable attention dating back to a question of Praeger in 1990. It was shown by Giudici and Xia that the smallest upper bound on $s$ is attained for some digraph admitting an almost simple $s$-arc-transitive group. In this paper, based on the work of Pan, Wu and Yin, we prove that $s\leqslant 2$ in the case where the group is an alternating or symmetric group. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2111_06579 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Bounding $s$ for vertex-primitive $s$-arc-transitive digraphs of alternating and symmetric groups Chen, Junyan Chen, Lei Giudici, Michael Li, Jing Jian Praeger, Cheryl E. Xia, Binzhou Combinatorics Determining an upper bound on $s$ for finite vertex-primitive $s$-arc-transitive digraphs has received considerable attention dating back to a question of Praeger in 1990. It was shown by Giudici and Xia that the smallest upper bound on $s$ is attained for some digraph admitting an almost simple $s$-arc-transitive group. In this paper, based on the work of Pan, Wu and Yin, we prove that $s\leqslant 2$ in the case where the group is an alternating or symmetric group. |
| title | Bounding $s$ for vertex-primitive $s$-arc-transitive digraphs of alternating and symmetric groups |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2111.06579 |