The affine planeAG(2,q),q odd,has a unique one point extension |
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| Authors: | J. A. Thas |
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| Affiliation: | (1) Department of Pure Mathematics and Computer Algebra, University of Gent, Krijgslaan 281, B-9000 Gent, Belgium |
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| Abstract: | Summary LetJ be a finite inversive plane of odd orderq. If for at least one pointp ofJ the internal affine planeJp is Desarguesian, thenJ is Miquelian. Other formulation: the finite Desarguesian affine plane of odd orderq has a unique one point extension; this extension is the Miquelian inversive plane of orderq. It follows that there is a unique inversive plane of orderq, withq {3, 5, 7}.Oblatum 23-X-1992 & 24-I-1994 |
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