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arXiv · 2111.06579

Bounding $s$ for vertex-primitive $s$-arc-transitive digraphs of alternating and symmetric groups

Junyan Chen·Lei Chen·Michael Giudici·Jing Jian Li·Cheryl E. Praeger·Binzhou Xia
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Abstract

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.

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Junyan Chen, Lei Chen, Michael Giudici, Jing Jian Li, Cheryl E. Praeger, Binzhou Xia. 2021-11-12. Bounding $s$ for vertex-primitive $s$-arc-transitive digraphs of alternating and symmetric groups. https://arxiv.org/abs/2111.06579

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