Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Guo, Junying, Liu, Yanjun, Xiong, Huan
Institutions: Jiangxi Normal University, Harbin Institute of Technology
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1844031539, G4611506324
OpenAlex ID: W7220956545