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Paper   IPM / M / 8119
School of Mathematics
  Title:   3-designs from PGL(2,q)
1.  P. J. Cameron
2.  G. R. Omidi
3.  B. Tayfeh-Rezaie
  Status:   Published
  Journal: The Electronic Journal of Combinatorics
  Vol.:  13
  Year:  2006
  Pages:   #R50
  Supported by:  IPM
The group \PGL(2,q), q=pn, p an odd prime, is 3-transitive on the projective line and therefore it can be used to construct 3-designs. In this paper, we determine the sizes of orbits from the action of \PGL(2,q) on the k-subsets of the projective line when k is not congruent to 0 and 1 modulo p. Consequently, we find all values of λ for which there exist 3-(q+1,k,λ) designs admitting \PGL(2,q) as automorphism group. In the case p ≡ 3 mod 4, the results and some previously known facts are used to classify 3-designs from \PSL(2,p) up to isomorphism.

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