Geodesic
Generalised polygons admitting a point-primitive almost simple group of Suzuki or Ree type
Luke Morgan1 ; Tomasz Popiel1
1The University of Western Australia
The electronic journal of combinatorics, Tome 23 (2016) no. 1
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Let $G$ be a collineation group of a thick finite generalised hexagon or generalised octagon $\Gamma$. If $G$ acts primitively on the points of $\Gamma$, then a recent result of Bamberg et al. shows that $G$ must be an almost simple group of Lie type. We show that, furthermore, the minimal normal subgroup $S$ of $G$ cannot be a Suzuki group or a Ree group of type $^2\mathrm{G}_2$, and that if $S$ is a Ree group of type $^2\mathrm{F}_4$, then $\Gamma$ is (up to point-line duality) the classical Ree-Tits generalised octagon.
DOI : 10.37236/5510
Classification : 51E12, 20B15, 05B25
Mots-clés : generalised hexagon, generalised octagon, primitive permutation group

Luke Morgan  1   ; Tomasz Popiel  1

1 The University of Western Australia 
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Luke Morgan; Tomasz Popiel. Generalised polygons admitting a point-primitive almost simple group of Suzuki or Ree type. The electronic journal of combinatorics, Tome 23 (2016) no. 1. doi: 10.37236/5510

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