Vertex-primitive s-arc-transitive digraphs of linear groups

Michael Giudici; Cai Heng Li; Binzhou Xia

Journal article

Vertex-primitive s-arc-transitive digraphs of linear groups

Michael Giudici, Cai Heng Li, Binzhou Xia

JOURNAL OF PURE AND APPLIED ALGEBRA | ELSEVIER SCIENCE BV | Published : 2019

DOI: 10.1016/j.jpaa.2019.04.009

Abstract

We study G-vertex-primitive and (G,s)-arc-transitive digraphs for almost simple groups G with socle PSLn(q). We prove that s⩽2 for such digraphs, which provides the first step in determining an upper bound on s for all the vertex-primitive s-arc-transitive digraphs.

University of Melbourne Researchers

Binzhou Xia Author Mathematics and Statistics

Grants

Awarded by Australian Research Council

Awarded by NNSFC

Funding Acknowledgements

This research was supported by Australian Research Council grant DP150101066. The third author's work on this paper was done when he was a research associate at the University of Western Australia. The second author acknowledges the support of NNSFC grant 11771200. The authors would like to thank the anonymous referee for careful reading and valuable suggestions.