PreprintCC BY 4.0arXiv
Large Ree groups acting point and line-primitively on finite generalised quadrangles
Abstract
Suppose we have a finite thick generalised quadrangle whose automorphism group G acts primitively on both the set of points and the set of lines. Then G must be almost simple. Furthermore, soc(G) cannot be isomorphic to 2 B2(22m+1) or 2 G2(32m+1), where m is a positive integer. In this paper, we show that soc(G) cannot be isomorphic to 2 F4(22m+1).
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BibTeX
@misc{arumugam2026large,
title = {{Large Ree groups acting point and line-primitively on finite generalised quadrangles}},
author = {Vishnuram Arumugam},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39690},
eprint = {2610.39690},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39690},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Large Ree groups acting point and line-primitively on finite generalised quadrangles
AU - Vishnuram Arumugam
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39690
UR - https://arxiv.org/abs/2610.39690
AB - Suppose we have a finite thick generalised quadrangle whose automorphism group G acts primitively on both the set of points and the set of lines. Then G must be almost simple. Furthermore, soc(G) cannot be isomorphic to ^2 B_2(2^2m+1) or ^2 G_2(3^2m+1), where m is a positive integer. In this paper, we show that soc(G) cannot be isomorphic to ^2 F_4(2^2m+1).
ER -