Year: 2026
Type: preprint
Abstract: The classification of symmetric Cayley graphs has attracted considerable attention. Results have been obtained for finite abelian groups and nonabelian simple groups. However, the problem remains open for finite nonabelian characteristically simple groups, although some results on normality for small valencies are known. In this paper, we determine the possible structures of automorphism groups $X$ of connected 2-arc-transitive Cayley graphs $Γ$ of $G\cong T^k$, where $T$ is a finite nonabelian simple group and $k\geqslant2$. In the quasiprimitive case, we prove that $G\unlhd X$, $Γ$ is complete, or $X$ is of product action type with restricted parameters. For the non-quasiprimitive case, we determine the possible structures of the quasiprimitive normal quotients of $Γ$.
Source: arXiv (Cornell University)
Authors: Deng, Feng, Li, Jing Jian, Yu, Hao
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G4875178305, G6621321729
OpenAlex ID: W7223810480