﻿ 仿射型群与旗传递6-(v, k, 3)设计 Affine Type Groups and Flag-Transitive 6-(v, k, 3) Designs

Pure Mathematics
Vol.07 No.03(2017), Article ID:20519,4 pages
10.12677/PM.2017.73020

Affine Type Groups and Flag-Transitive 6-(v, k, 3) Designs

Xiaolian Liao, Guohua Chen

Department of Mathematics and Finance, Hunan Institute of Humanities Science and Technology, Loudi Hunan

Received: Apr. 28th, 2017; accepted: May 12th, 2017; published: May 16th, 2017

ABSTRACT

The classification of flag-transitive designs is an important subject on algebraic combinatorics. And the automorphism groups of a flag-transitive 6-(v, k, 3) design are 3-homogeneous. Therefore, using the classification theorem of 3-homogeneous permutation groups, the classification of flag-transitive 6-(v, k, 3) designs can be discussed, and we prove that the automorphism groups of a flag-transitive 6-(v, k, 3) design are not isomorphic to affine type groups.

Keywords:Flag-Transitive, 3 -Homogeneous Groups, Permutation Group, Affine Group

Email: hnldlxl2005@126.com

1. 引言

2. 预备知识

(1) 如果D的自同构群G区–传递地作用于上，则必点-齐次地作用于上;

(2) 如果D的自同构群G旗–传递地作用于上，则必点-齐次地作用于上。

(1)

(2);

(3) 如果t = 6，那么.

(1)

(2)

(3)

3. 主要定理的证明

，且

(1)

Affine Type Groups and Flag-Transitive 6-(v, k, 3) Designs[J]. 理论数学, 2017, 07(03): 159-162. http://dx.doi.org/10.12677/PM.2017.73020

1. 1. Biggs, N.L. and Whit, E.A.T. (1979) Permutation Groups and Combinatorial Structures. Peking University Press, Beijing, 2-32. https://doi.org/10.1017/cbo9780511600739

2. 2. Cameron, P.J. and Praeger, C.E. (1992) Block-Transitive t-Designs. Finite Geometry and Combinatorics, 191, 103-119.

3. 3. Beth, T., Jungnickel, D. and Lenz, H. (1999) Design Theory. Cambridge University Press, Cambridge, 3-28.

4. 4. Huber, M. (2007) A Sensus of Highly Symmetric Combinatorial Designs. Journal of Algebraic Combinatorics, 26, 453-476. https://doi.org/10.1007/s10801-007-0065-4

5. 5. 徐向红, 章静. 3-齐次群与旗传递 5-(v,k,3)设计[J]. 数学理论与应用, 2009, 32(04): 5-11.