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- W3113201211 abstract "We discuss recent progress on the problem of classifying point-primitive generalised polygons. In the case of generalised hexagons and generalised octagons, this has reduced the problem to primitive actions of almost simple groups of Lie type. To illustrate how the natural geometry of these groups may be used in this study, we show that if $mathcal{S}$ is a finite thick generalised hexagon or octagon with $G leqslant{rm Aut}(mathcal{S})$ acting point-primitively and the socle of $G$ isomorphic to ${rm PSL}_n(q)$ where $n geqslant 2$, then the stabiliser of a point acts irreducibly on the natural module. We describe a strategy to prove that such a generalised hexagon or octagon $mathcal{S}$ does not exist." @default.
- W3113201211 created "2020-12-21" @default.
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- W3113201211 date "2020-12-07" @default.
- W3113201211 modified "2023-09-23" @default.
- W3113201211 title "Point-primitive generalised hexagons and octagons and projective linear groups" @default.
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- W3113201211 doi "https://doi.org/10.48550/arxiv.2012.04189" @default.
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