Določanje zgornje meje za s pri točkovno primitivnih s-ločno tranzitivnih digrafih alternirajočih in simetričnih grup

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.