Quadruple systems over Zp admitting the affine group

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


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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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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