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Quadruple systems over Zp admitting the affine group

  • Egmont Köhler
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 969)

Abstract

A necessary and sufficient condition for the existence of t-(p,k,λ) designs which are invariant under the affine group Ap={x → ax+b : a,b ε GF(p), a ≠ 0} is given. From this we derive sufficient criteria für the existence of Ap-invariant 3-(p,4,λ) designs for all primes p. These designs are simple in the case p ≡ 5(mod 12) and λ=2. As a corollary to our considerations, we obtain some infinite series of simple 2-(p,r,λ) designs for all primes p and certain values of λ which are also invariant under Ap.

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References

  1. 1.
    J. Doyen A. Rosa An extended bibliography and survey of Steiner systems. Annals of Discr.Math., 7, 1980, 317–349.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    M.Kleemann k-Differenzenkreise und zweifach ausgewogene Pläne. Diplomarbeit, Univ. Hamburg, 1980.Google Scholar
  3. 3.
    E. Köhler Zur Theorie der Steinersysteme. Abh.Math.Sem. Univ.Hamburg, 43, 1975, 181–185.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    E. Köhler Zyklische Quadrupelsysteme. Abh.Math.Sem. Univ.Hamburg, 48, 1979, 1–24.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    E. Köhler Numerische Existenzkriterien in der Kombinatorik. Numerische Methoden bei graphentheoretischen und kombinatorischen Problemen. Birkhäuser, Basel, 1975, 99–108.Google Scholar
  6. 6.
    E. Köhler k-Differencecycles and the Construction of Cyclic t-Designs in: Geometries and Groups. Lecture Notes in Mathematics, 893, 1981, 195–203, Berlin-Heidelberg-New York.CrossRefGoogle Scholar
  7. 7.
    C. Lindner R. Rosa Steiner Quadrupel Systems. Discrete Math., 22, 1978, 147–181.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Egmont Köhler
    • 1
  1. 1.Mathematisches Seminar der Universität HamburgHamburg 12Federal Republic of Germany

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