Symmetric Cayley graphs on non-abelian simple groups of valency 7

2024/09/28 by Zhang, Xing, Feng, Yan-Quan, Yin, Fu-Gang +1
#05C25 #20B25 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2409.19225

Abstract

Let Γ be a connected 7-valent symmetric Cayley graph on a finite non-abelian simple group G. If Γ is not normal, Li \em et al. [On 7-valent symmetric Cayley graphs of finite simple groups, J. Algebraic Combin. 56 (2022) 1097-1118] characterised the group pairs (soc(Aut(Γ)/K),GK/K), where K is a maximal intransitive normal subgroup of Aut(Γ). In this paper, we improve this result by proving that if Γ is not normal, then Aut(Γ) contains an arc-transitive non-abelian simple normal subgroup T such that G

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