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Bounding s for vertex-primitive s-arc-transitive digraphs of alternating and symmetric groupsJunyan Chen,
Lei Chen,
Michael Giudici,
Jing Jian Li,
Cheryl E. Praeger,
Binzhou Xia, 2025, original scientific article
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<=2 in the case where the group is an alternating or symmetric group.
Keywords: digraph, vertex-primitive, s-arc-transitive, alternating group, symmetric group
Published in RUP: 22.10.2025; Views: 391; Downloads: 3
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