Year: 2026
Type: preprint
Abstract: Keller and Yang formulated two conjectures relating abelian quotients of subgroups of finite linear groups to largest orbit sizes. After counterexamples were found to the original conjectures, two revised versions were proposed. We prove both revised conjectures for every finite group $G$ satisfying $F(G)=F^*(G)$. We also extend a regular-orbit theorem for nilpotent subgroups to completely reducible modules of mixed characteristic under the same hypothesis.
Source: arXiv (Cornell University)
Author: Yang, Yong
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223875876