Polarities and planar collineations of Moufang planes

We show that conjugacy classes of Baer involutions and non-elliptic polarities, respectively, of proper (i.e., non-desarguesian) Moufang planes are interrelated. Restriction of the conjugating group to the stabilizer of a triangle or a quadrangle does not refine the classes. These results are applie...

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Bibliographic Details
Published in:Monatshefte für Mathematik 2013-03, Vol.169 (3-4), p.383-395
Main Authors: Knarr, Norbert, Stroppel, Markus
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We show that conjugacy classes of Baer involutions and non-elliptic polarities, respectively, of proper (i.e., non-desarguesian) Moufang planes are interrelated. Restriction of the conjugating group to the stabilizer of a triangle or a quadrangle does not refine the classes. These results are applied to prove transitivity properties for the centralizers of these polarities. Along the way, a new proof is obtained for the fact that the automorphism group of a Moufang plane acts transitively on quadrangles.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-012-0409-6