A note on Huppert's theorem and Chen's theorem

  • Jiangtao Shi

    Yantai University, China
  • Mengjiao Shan

    Yantai University, China
  • Fanjie Xu

    Yantai University, China
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Abstract

Let be a finite group. We prove that every maximal subgroup of has prime index if and only if every maximal subgroup of that contains the normalizer of some Sylow subgroup has prime index, which implies that the hypothesis in Huppert's theorem and the hypothesis in Chen's theorem are actually equivalent. Moreover, we prove that the hypothesis in a theorem of Shao and Beltrán and the hypothesis in a theorem of Li et al. are also equivalent.

Cite this article

Jiangtao Shi, Mengjiao Shan, Fanjie Xu, A note on Huppert's theorem and Chen's theorem. Rend. Sem. Mat. Univ. Padova 153 (2025), pp. 243–247

DOI 10.4171/RSMUP/153