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ON SYLOW-COVERS OF CUBIC ARC-TRANSITIVE GRAPHS
Keywords:
arc-transitive graph, vertex stabilizer, normal subgroup, Sylow-coverDOI:
https://doi.org/10.17654/0972555525029Abstract
Let $\Gamma$ be a finite connected cubic $T$-arc-transitive graph, where $T \leq \operatorname{Aut}(\Gamma)$ is a nonabelian simple group. Let $p>|T|_2$ be an odd prime, and $(p,|T|)=1$. Then there exists a normal cover $\widetilde{\Gamma}$ of $\Gamma$ with $\operatorname{Aut}(\widetilde{\Gamma})=P . T$ and the covering transformation group $P \in \operatorname{Syl}_p(\operatorname{Aut}(\widetilde{\Gamma}))$.
Received: April 15, 2025
Revised: April 17, 2025
Accepted: July 28, 2025
References
[1] M. D. E. Conder and J. C. Ma, Arc-transitive abelian regular covers of cubic graphs, J. Algebra 387 (2013), 225-242.
[2] M. D. E. Conder and J. C. Ma, Arc-transitive abelian regular covers of the Heawood graph, J. Algebra 387 (2013), 243-267.
[3] M. Conder and R. Nedela, A refined classification of symmetric cubic graphs, J. Algebra 322 (2009), 722-740.
[4] S. F. Du, J. H. Kwak and M. Y. Xu, Linear criteria for lifting of automorphisms of elementary abelian regular coverings, Linear Algebra Appl. 373 (2003), 101-119.
[5] Y. Q. Feng and J. H. Kwak, Cubic symmetric graphs of order a small number times a prime or a prime square, J. Combin. Theory Ser. B 97 (2007), 627-646.
[6] B. Kuzman, Arc-transitive elementary abelian covers of the complete graph K5, Linear Algebra Appl. 433 (2010), 1909-1921.
[7] J. H. Kwak and J. M. Oh, Arc-transitive elementary abelian covers of the octahedron graph, Linear Algebra Appl. 429 (2009), 2180-2198.
[8] J. C. Ma, Arc-transitive dihedral regular covers of cubic graphs, Electron. J. Combin. 21 (2014), P3.5.
[9] A. Malnič, D. Marušič and P. Potočnik, Elementary abelian covers of graphs, J. Algebraic Combin. 20(1) (2004), 71-97.
[10] P. Potočnik and P. Spiga, Lifting a prescribed group of automorphisms of graphs, Proc. Amer. Math. Soc. 147(9) (2019), 3787-3796.
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