.2 - (v, K And ¦Ë) Symmetric Design Of The Flag Is Passed From The Same Automorphism Group,

After the classification of flag-transitive linear spaces, attention has now turned to the flag-transitive automorphism groups. The research on flag-transitive automorphism groups is the forefront subject of the finite groups theory and algebra combinatorial theory. This thesis has acquired some new conclusions on it.t - designs is a very important class of combinatorial designs. Eugenia and his students have discussed the t-(v,k,λ)(t = 2) symmetric designs. They have acquired the conclusions that the flag-transitive, primitive automorphism groups of a non-trivial 2-(v,k,λ) symmetric designs withλ≤3 must be affine type or almost simple type. They have completed the classification of the flag-transitive, primitive automorphism groups of a non-trivial 2-(v,k,2) symmetric designs. Based on their researches, we will furtherly consider the 2-(v,k,λ)(λ=3,4) symmetric designs.This thesis consists of three chapters.In chapter 1, we will give some introduction about the history and current research situation of the group theory and design (linear spaces) theory. Then we can realize of the development situation about this research fields and the relations between the group theory and design (linear spaces) theory.In chapter 2 , we will introduce the elementary concepts and conclusions that will be used in this thesis. Then we can construct the basic theory system of this thesis.Chapter 3 is the focus of this thesis . In this chapter, the characters of symmetric designs is mentioned. We also will give the structures and characters of some almost simple groups, and discuss the flag-transitive automorphism groups of symmetric designs is almost simple type situation. Then, we get the main theorem as follows:Main Theorem (1) If G is a flag-transitive, primitive automorphi-sm group of a non-trivial 2-(v,k,3) symmetric design, then the socle of G is't ²F₄(q²) group, G₂(q) group, and ³D₄(q) group.(2) If G is a flag-transitive, primitive automorphism group of a non-trivial 2-(v,k,4) symmetric design, then G is of affine, or almost simple type.