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- Title
The correlations of finite Desarguesian planes, Part IV: The classification (III).
- Authors
Kestenband, Barbu C.
- Abstract
This paper is the last in a series of four articles devoted to the classification of correlations of finite Desarguesian planes of odd nonsquare order. The first three papers (see references [7], [8], [9]) were devoted to correlations whose squares (which are, of course, collineations) leave invariant at least one nonabsolute point of the respective correlation. The present article discusses the “singular” situation in which the square of a correlation does not fix any nonabsolute point of that correlation. It turns out that there is, up to isomorphisms, just one such correlation, and that it possesses q2 n+1 + 1 absolute points. Its square leaves invariant one absolute point.
- Subjects
DESARGUESIAN planes; AFFINE geometry; PROJECTIVE geometry; SET theory; TOPOLOGY; HYPERSETS
- Publication
Journal of Geometry, 2007, Vol 86, Issue 1/2, p98
- ISSN
0047-2468
- Publication type
Article
- DOI
10.1007/s00022-006-1893-4