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arXiv · 1410.3423

Point-primitive generalised hexagons and octagons

John Bamberg·S. P. Glasby·Tomasz Popiel·Cheryl E. Praeger·Csaba Schneider
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Abstract

In 2008, Schneider and Van Maldeghem proved that if a group acts flag-transitively, point-primitively, and line-primitively on a generalised hexagon or generalised octagon, then it is an almost simple group of Lie type. We show that point-primitivity is sufficient for the same conclusion, regardless of the action on lines or flags. This result narrows the search for generalised hexagons or octagons with point- or line-primitive collineation groups beyond the classical examples, namely the two generalised hexagons and one generalised octagon admitting the Lie type groups $\mathsf{G}_2(q)$, $\,^3\mathsf{D}_4(q)$, and $\,^2\mathsf{F}_4(q)$, respectively.

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John Bamberg, S. P. Glasby, Tomasz Popiel, Cheryl E. Praeger, Csaba Schneider. 2014-10-09. Point-primitive generalised hexagons and octagons. https://arxiv.org/abs/1410.3423

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