Abstract
In this article we consider a sub-geometry G of the D4 building geometry whose flags of type {1, 3, 4} are exactly those which are opposite to their image under a triality on D4, while the lines of G are certain so-called skew lines (see Definition 3.4). We prove that this rank four geometry G admits the group G2 as a flag-transitive group of automorphisms. Moreover, if the underlying field contains at least three elements, the geometry G is simply connected. Accordingly, we obtain an amalgam presentation of G2 via the rank one and two parabolics of the action of G2 on G .
Original language | English |
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Pages (from-to) | 491-510 |
Number of pages | 4 |
Journal | Journal of Group Theory |
Volume | 12 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2009 |