
doi: 10.1007/bf01263474
This article gives examples of 8-dimensional symmetric planes with nondesarguesian tangent translation planes. Up to now all known examples of (nonabelian) symmetric planes are open subplanes of a classical projective plane over an alternative real division algebra \(F\). That is, the algebra \(F\) is the reals \(\mathbb{R}\), the complexes \(\mathbb{C}\), the quaternions \(\mathbb{H}\), or the octonions \(\mathbb{O}\). In these examples a tangent translation plane is just the affine plane over \(F\). The examples constructed by the author are obtained by starting with a dual projective plane over certain locally connected nearfield and removing first the line at infinity and then the line \(x = 0\). The resulting complement is a symmetric plane which has nondesarguesian tangent translation planes.
8-dimensional symmetric planes, tangent translation planes, Topological linear incidence structures
8-dimensional symmetric planes, tangent translation planes, Topological linear incidence structures
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