On a class of affine geometries

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Abstract

The far-away geometry ∑ in a symplectic polar space is the subgeometry on the points non-collinear to a fixed point. In case of the polar space of rank three we define a class of subgeometries of ∑ with the same points and lines as ∑ and some of the planes of ∑ removed. We show that such geometries are simply connected, unless ∑ is defined over GF(2). As an application, for a particular such subgeometry Γ we exhibit a flag-transitive group G and, as a result, we get an amalgam presentation for this G. The smallest instance (over GF(3)) of G is related to the sporadic Thompson simple group.

Details

Original languageEnglish
Pages (from-to)381-399
Number of pages19
JournalAdvances in Geometry
Volume12
Issue number3
Publication statusPublished - 1 Sep 2012