Geodesic
Low rank groups of Lie type acting point- and line-primitively on finite generalised quadrangles
Vishnuram Arumugam1 ; John Bamberg1 ; Michael Giudici1
1University of Western Australia
The electronic journal of combinatorics, Tome 32 (2025) no. 1
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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. In this paper, we show that $\operatorname{soc}(G)$ cannot be isomorphic to $\operatorname{Sz}(2^{2m+1})$ or $\operatorname{Ree}(3^{2m+1})$ where $m$ is a positive integer.
DOI : 10.37236/12993
Classification : 20B25, 51E12
Mots-clés : generalized quadrangle, Suzuki groups, Ree groups, primitive groups

Vishnuram Arumugam  1   ; John Bamberg  1   ; Michael Giudici  1

1 University of Western Australia 
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     author = {Vishnuram Arumugam and John Bamberg and Michael Giudici},
     title = {Low rank groups of {Lie} type acting point- and line-primitively on finite generalised quadrangles},
     journal = {The electronic journal of combinatorics},
     year = {2025},
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Vishnuram Arumugam; John Bamberg; Michael Giudici. Low rank groups of Lie type acting point- and line-primitively on finite generalised quadrangles. The electronic journal of combinatorics, Tome 32 (2025) no. 1. doi: 10.37236/12993

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