3-(q + 1, 4, λ) Designs Of The Maximal Subgroups Of PSL(2, Q)

Combinatorial design theory has been an active research area for the more than fifty years. Combinatorial designs have important applications in many disciplines including coding theory, finite geometry, operation research and information science.The t-Designs play a central role in combinatorial design theory. In the literature of design theory, various algebraic structures have been employed to the constructions of t-designs. In this thesis, we are concerned with t-designs having an intransitive group actions on the point sets. To be precise, the point sets are projective lines and groups are maximal subgroups of PSL（2, q） for some specific values of q.Firstly, we discuss the existence of 3-designs with automorphism groups the maximum subgroups of PSL（2, 9）. Secondly, we study the existence of simple 3-designs with automorphism group the point stabilizers. Thirdly, we discuss the existence of simple3-designs with automorphism group PGL（2, q₀）, where q is a power of q₀. Finally, we discuss the existence of simple 3-designs with automorphism groups the dihedral group.