The Classification of Flag-transitive Steiner 5-Designs

Abstract

In this chapter, we present the complete classification of all flag-transitive Steiner 5-designs. The result relies on the classification of the finite 3-homogeneous permutation groups, which itself depends on the finite simple group classification (see Chapter 2). With regard to Section 2.2, we may consider two types of 3-homogeneous permutation groups. Specifically, as in the previous chapter the groups of almost simple type with the projective group PSL(2, q) as simple normal subgroup need extensive consideration.