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PreprintarXiv licencearXiv

Finite groups whose proper subgroups of order divisible by p are supersolvable

  • Antonio Beltrán
  • Fernando Viudez
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Abstract

Let p be an odd prime, and let G be a finite group whose order is divisible by p. Suppose that every proper subgroup of G whose order is divisible by p is supersolvable, while G itself is not. In this paper, we investigate the arithmetic and structural properties of such groups, addressing both the solvable and nonsolvable cases.

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Cite

BibTeXRIS
BibTeX
@misc{beltran2026finite,
  title = {{Finite groups whose proper subgroups of order divisible by $p$ are supersolvable}},
  author = {Antonio Beltrán and Fernando Viudez},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.09144},
  eprint = {2607.09144},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.09144},
}
RIS
TY  - UNPB
TI  - Finite groups whose proper subgroups of order divisible by p are supersolvable
AU  - Antonio Beltrán
AU  - Fernando Viudez
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2607.09144
UR  - https://arxiv.org/abs/2607.09144
AB  - Let p be an odd prime, and let G be a finite group whose order is divisible by p. Suppose that every proper subgroup of G whose order is divisible by p is supersolvable, while G itself is not. In this paper, we investigate the arithmetic and structural properties of such groups, addressing both the solvable and nonsolvable cases.
ER  -