Journal of Lie Theory 24 (2014), No. 1, 123--146
Copyright Heldermann Verlag 2014
8-Dimensional Compact Planes with an Automorphism Group which has a Normal Vector Subgroup
Helmut Salzmann
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
helmut.salzmann@uni-tuebingen.de
A connected group Δ of automorphisms of an 8-dimensional compact plane P fixes at most some collinear points or 2 points and 2 lines (double flag). For each possible configuration of fixed elements of a group of sufficiently large dimension the structure of Δ and its action on P is determined. Examples are given; in the case of a double flag, all planes are described explicitly.
Keywords: Compact projective plane, Lie collineation group, elation, straight, dimension.
MSC: 51H10
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