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- W2964034801 abstract "Abstract Let G be a group of collineations of a finite thick generalised quadrangle Γ. Suppose that G acts primitively on the point set <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>𝒫</m:mi> </m:math> ${mathcal{P}}$ of Γ, and transitively on the lines of Γ. We show that the primitive action of G on <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>𝒫</m:mi> </m:math> ${mathcal{P}}$ cannot be of holomorph simple or holomorph compound type. In joint work with Glasby, we have previously classified the examples Γ for which the action of G on <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>𝒫</m:mi> </m:math> ${mathcal{P}}$ is of affine type. The problem of classifying generalised quadrangles with a point-primitive, line-transitive collineation group is therefore reduced to the case where there is a unique minimal normal subgroup M and M is non-Abelian." @default.
- W2964034801 created "2019-07-30" @default.
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- W2964034801 date "2016-09-14" @default.
- W2964034801 modified "2023-10-13" @default.
- W2964034801 title "Point-primitive, line-transitive generalised quadrangles of holomorph type" @default.
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- W2964034801 doi "https://doi.org/10.1515/jgth-2016-0042" @default.
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