TITLE:
Flag-Transitive 6-(v, k, 2) Designs
AUTHORS:
Xiaolian Liao, Shangzhao Li, Guohua Chen
KEYWORDS:
Flag-Transitive, Combinatorial Design, Permutation Group, Affine Group, 3-Homogeneous Permutation Groups
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.4 No.5,
May
12,
2014
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.