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

Mathematical and Computational Applications

Liao, Xiaolian¹ 

关键词: block-transitive;    3-homogeneous groups;    permutation group;    Affine Type Groups;    Almost Simple Type Groups;   

DOI  :  10.3390/mca22020035

学科分类：计算数学

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY