Vertex-primitive s-arc-transitive digraphs of alternating and symmetric groups
Combinatorics
2018-10-23 v1 Group Theory
Abstract
A fascinating problem on digraphs is the existence problem of the finiteupper bound on s for all vertex-primitive s-arc-transitive digraphs except directed cycles (which is known to be reduced to the almost simple groups case). In this paper,we prove that s 2 for all G-vertex-primitive s-arc-transitive digraphs with G an (insoluble) alternating or symmetric group, which makes an important progress towards a solution of the problem. The proofs involves some methods that may be used to investigate other almost simple groups cases.
Keywords
Cite
@article{arxiv.1810.08909,
title = {Vertex-primitive s-arc-transitive digraphs of alternating and symmetric groups},
author = {Jiangmin Pan and Cixuan Wu and Fugang Yin},
journal= {arXiv preprint arXiv:1810.08909},
year = {2018}
}