Flag-Transitive 6-(v, k, 2) Designs

Xiaolian Liao, Shangzhao Li, Guohua Chen

Department of Mathematics, Changshu Institute of Technology, Changshu, China.
Department of Mathematics, Hunan University of Humanities Science and Technology, Loudi, China.

DOI: 10.4236/apm.2014.45026                

Abstract

The automorphism group of a flag-transitive 6–(v, k, 2) design is a 3-homogeneous permutation group. Therefore, using the classification theorem of 3–homogeneous permutation groups, the classification of flag-transitive 6-(v, k,2) designs can be discussed. In this paper, by analyzing the combination quantity relation of 6–(v, k, 2) design and the characteristics of 3-homogeneous permutation groups, it is proved that: there are no 6–(v, k, 2) designs D admitting a flag transitive group G ≤ Aut (D) of automorphisms.

Keywords

Flag-Transitive, Combinatorial Design, Permutation Group, Affine Group, 3-Homogeneous Permutation Groups

Conflicts of Interest

The authors declare no conflicts of interest.

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