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PreprintCC BY 4.0arXiv

A Counterexample to a Conjecture of Moreto

  • Gang Chen
  • Wenhua Zhao
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Abstract

As an extension of the It^o-Michler theorem to the nonabelian or nonnormal Sylow subgroups, A. Moreto raised the following conjecture: let G be a finite group and P a Sylow p-subgroup of G. Then the number of irreducible characters of G whose degrees are divisible by p is not less than the length of any subgroup chain between N_G(P) and G. In this short note, we give a counterexample to this conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026counterexample,
  title = {{A Counterexample to a Conjecture of Moreto}},
  author = {Gang Chen and Wenhua Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26471},
  eprint = {2609.26471},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26471},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Counterexample to a Conjecture of Moreto
AU  - Gang Chen
AU  - Wenhua Zhao
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26471
UR  - https://arxiv.org/abs/2609.26471
AB  - As an extension of the It^o-Michler theorem to the nonabelian or nonnormal Sylow subgroups, A. Moreto raised the following conjecture: let G be a finite group and P a Sylow p-subgroup of G. Then the number of irreducible characters of G whose degrees are divisible by p is not less than the length of any subgroup chain between N_G(P) and G. In this short note, we give a counterexample to this conjecture.
ER  -