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A characterization of Thalesian orthogonality in Pappian planes of characteristic 2

✍ Scribed by Ralph-Hardo Schulz

Publisher
Springer
Year
1982
Tongue
English
Weight
292 KB
Volume
13
Category
Article
ISSN
0046-5755

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✦ Synopsis

In an affine plane over a field K, any Thalesian orthogonality relation is equivalent to Β±d for some deK{0}, where Β±d denotes the relation with constant of orthogonality d (i.e., after suitable coordinatization the slopes m, m* E K\ {0} of orthogonal lines satisfy m-m* = d) (cf. [1], [5]). In the present paper we show that in a Pappian plane of characteristic two any orthogonality relation admitting the same group as L1 is equivalent to L1. This gives a characterization of Thalesian orthogonality over perfect fields of characteristic two.

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