On a Class of Symmetric Divisible Designs which are Almost Projective Planes View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2001

AUTHORS

Aart Blokhuis , Dieter Jungnickel , Bernhard Schmidt

ABSTRACT

We consider a class of symmetric divisible designs D which are almost projective planes in the following sense: Given any point p, there is a unique point p’ such that p and p’ are on two lines, whereas any other point is joined to p by exactly one line; and dually. We note that either the block size k or k — 2 is a perfect square, and exhibit examples for k =3 and k = 4. Then we add the condition that D should admit an abelian Singer group, so that we may study the associated divisible difference sets. Under this additional assumption, we show that k is a square (unless k = 3) and that the only possible prime divisors of k are 2 and 3. More... »

PAGES

27-34

References to SciGraph publications

  • 1989-11. On abelian difference sets with multiplier — 1 in ARCHIV DER MATHEMATIK
  • 1991-09. The mann test for divisible difference sets in GRAPHS AND COMBINATORICS
  • 1995. Finite Geometry and Character Theory in NONE
  • 1954-04. Verallgemeinerung einesFermatschen Satzes in ARCHIV DER MATHEMATIK
  • Book

    TITLE

    Finite Geometries

    ISBN

    978-1-4613-7977-5
    978-1-4613-0283-4

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-1-4613-0283-4_2

    DOI

    http://dx.doi.org/10.1007/978-1-4613-0283-4_2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1027263095


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