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Abelian composition factors of finite rational groups

  • Junying Guo
  • Yanjun Liu
  • Huan Xiong
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Abstract

Motivated by an observation concerning the S3-conjecture, we prove that every abelian composition factor of a finite rational group has order $2$, $3$, or $5$. Thompson previously restricted these orders to {2,3,5,7,11}; we exclude $7$ and $11$, establishing the bound that he proposed. Together with the work of Feit and Seitz on nonabelian composition factors, this completes the determination of the possible composition factors of finite rational groups.

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Cite

BibTeXRIS
BibTeX
@misc{guo2026abelian,
  title = {{Abelian composition factors of finite rational groups}},
  author = {Junying Guo and Yanjun Liu and Huan Xiong},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09368},
  eprint = {2610.09368},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09368},
}
RIS
TY  - UNPB
TI  - Abelian composition factors of finite rational groups
AU  - Junying Guo
AU  - Yanjun Liu
AU  - Huan Xiong
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.09368
UR  - https://arxiv.org/abs/2610.09368
AB  - Motivated by an observation concerning the S_3-conjecture, we prove that every abelian composition factor of a finite rational group has order $2$, $3$, or $5$. Thompson previously restricted these orders to {2,3,5,7,11}; we exclude $7$ and $11$, establishing the bound that he proposed. Together with the work of Feit and Seitz on nonabelian composition factors, this completes the determination of the possible composition factors of finite rational groups.
ER  -