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On 2-Arc-Transitive Cayley Graphs of Nonabelian Characteristically Simple Groups

  • Feng Deng
  • Jing Jian Li
  • Hao Yu
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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≅ Tk, where T is a finite nonabelian simple group and kgeqslant2. In the quasiprimitive case, we prove that Gunlhd 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.

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Cite

BibTeXRIS
BibTeX
@misc{deng20262arctransitive,
  title = {{On 2-Arc-Transitive Cayley Graphs of Nonabelian Characteristically Simple Groups}},
  author = {Feng Deng and Jing Jian Li and Hao Yu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33978},
  eprint = {2610.33978},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33978},
}
RIS
TY  - UNPB
TI  - On 2-Arc-Transitive Cayley Graphs of Nonabelian Characteristically Simple Groups
AU  - Feng Deng
AU  - Jing Jian Li
AU  - Hao Yu
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.33978
UR  - https://arxiv.org/abs/2610.33978
AB  - 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≅ T^k, where T is a finite nonabelian simple group and kgeqslant2. In the quasiprimitive case, we prove that Gunlhd 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.
ER  -