3-Homogeneous Groups and Block-Transitive 7–(v, k, 3) Designs

Abstract

The classification of a block-transitive designs is an important subject on algebraic combinatorics. With the aid of MATLAB software, using the classification theorem of 3-homogeneous permutation groups, we look at the classification problem of block-transitive 7–(v, k, 3) design and prove our main theorem: If the automorphism group of a 7–(v, k, 3) design is block-transitive, then it is neither isomorphic to Affine Type Groups nor Almost Simple Type Groups.

Keywords

• block-transitive
• 3-homogeneous groups
• permutation group
• Affine Type Groups
• Almost Simple Type Groups