Partial geometries pg (s, t, 2) with an abelian Singer group and a characterization of the van Lint-Schrijver partial geometry |
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Authors: | S De Winter |
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Institution: | (1) Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, B-9000 Gent, Belgium |
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Abstract: | Let be a proper partial geometry pg(s,t,2), and let G be an abelian group of automorphisms of acting regularly on the points of . Then either t≡2±od
s+1 or is a pg(5,5,2) isomorphic to the partial geometry of van Lint and Schrijver (Combinatorica 1 (1981), 63–73). This result is a new step towards the classification of partial geometries with an abelian Singer group and further provides an interesting characterization of the geometry of van Lint and Schrijver.The author is Postdoctoral Fellow of the Fund for Scientific Research Flanders (FWO-Vlaanderen). |
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Keywords: | Partial geometry Abelian Singer group Geometry of van Lint-Schrijver |
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