On abstract ovals with Pascalian secant lines

John Bamberg; Tim Harris; Tim Penttila

doi:10.1515/jgth-2018-0028

On abstract ovals with Pascalian secant lines

John Bamberg, Tim Harris, Tim Penttila

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

63 Downloads (Pure)

Abstract

We prove that an abstract oval is an abstract conic if and only if all of its involutions are regular and all of its secant lines are Pascalian. In doing so, we provide a new characterisation of the rank 1 projective general linear groups over arbitrary fields.

Original language	English
Pages (from-to)	1051-1064
Number of pages	14
Journal	Journal of Group Theory
Volume	21
Issue number	6
DOIs	https://doi.org/10.1515/jgth-2018-0028
Publication status	Published - 1 Nov 2018

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10.1515/jgth-2018-0028

AAM_On abstract ovalsAccepted author manuscript, 348 KB

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On abstract ovals with Pascalian secant lines

Abstract

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Finite geometry from an algebraic point of view

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On abstract ovals with Pascalian secant lines

Abstract

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Finite geometry from an algebraic point of view

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