Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 30 min ago
PreprintCC BY 4.0arXiv

On a finite group in which every maximal subgroup of order divisible by p containing the normalizer of some Sylow subgroup is nilpotent

  • Jiangtao Shi
  • Fanghua Li
Open at sourcePDFDOICite

Abstract

Let G be a finite group and p any fixed prime divisor of |G|. We prove that if every maximal subgroup of G of order divisible by p containing the normalizer of some Sylow subgroup is nilpotent then G is a solvable group having a Sylow tower and G is q-nilpotent or q-closed for each prime divisor q of |G|.

Related

  1. On a finite group in which every non-nilpotent maximal invariant subgroup of order divisible by p is normal
    Jiangtao Shi, Fanghua Li, Na Li
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. On a finite group in which every non-supersolvable maximal subgroup is a TI-subgroup
    Jiangtao Shi, Fanghua Li
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Finite groups with simple or p-nilpotent maximal subgroups
    Antonio Beltrán, Fernando Viudez
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Maximal regular subsemigroups containing the group of units of transformation semigroups that preserve a uniform equivalence relation with two classes
    Kritsada Sangkhanan
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. On the centralizer and normalizer groups of odometers and Toeplitz subshifts
    Jaime Gómez, Samuel Petite
    arXivPreprintCC BY 4.0Full textDynamical systemsarXiv

Cite

BibTeXRIS
BibTeX
@misc{shi2026finite,
  title = {{On a finite group in which every maximal subgroup of order divisible by $p$ containing the normalizer of some Sylow subgroup is nilpotent}},
  author = {Jiangtao Shi and Fanghua Li},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02596},
  eprint = {2611.02596},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02596},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On a finite group in which every maximal subgroup of order divisible by p containing the normalizer of some Sylow subgroup is nilpotent
AU  - Jiangtao Shi
AU  - Fanghua Li
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02596
UR  - https://arxiv.org/abs/2611.02596
AB  - Let G be a finite group and p any fixed prime divisor of |G|. We prove that if every maximal subgroup of G of order divisible by p containing the normalizer of some Sylow subgroup is nilpotent then G is a solvable group having a Sylow tower and G is q-nilpotent or q-closed for each prime divisor q of |G|.
ER  -