Two-arc-transitive non-solvable covers of the Petersen graph

2025/03/10 by Jiyong Chen, Cai Heng Li, Chen, Jiyong +4
Mathematics · #05C38 #20B25 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2503.06979

openalex publication_date 2025/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that, for any \2,3\-generated perfect group P, there exists a 2-arc-transitive graph which has full automorphism group isomorphic to P\wr A₅=P⁵: A₅ and is a cover of the Petersen graph. This particularly shows that there are infinitely many 2-arc-transitive normal covers of the Petersen graph. To the best of our knowledge, these are the first known examples of 2-arc-transitive non-trivial covers of 2-arc-transitive graphs with non-solvable transformation groups. Moreover, these graphs are non-Cayley graphs, and have girth 10.

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