Miquelian inversive planes which admit an orthogonality both in the sense of Dembowski and Hughes and of Benz
✍ Scribed by Yves Mencerrey
- Publisher
- Springer
- Year
- 1988
- Tongue
- English
- Weight
- 178 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0046-5755
No coin nor oath required. For personal study only.
✦ Synopsis
The object of this article is to prove a necessary and sufficient condition such that the orthogonality defined by Dembowski and Hughes in the case of characteristic different from 2 (see [4]) satisifes the following axiom: Two orthogonal circles are secant. ° NOTATIONS. K designates a commutative field of characteristic different from 2; K* the set K -{0}; K 2 the set of squares in K; V a vector space of dimension 4 over K; and P(V) the associated 3-dimensional projective geometry. For convenience, we use the same notation for a vector subspace of V and the corresponding element of P(V). If p is a point of P(V), it will be