Unsolvable block transitive automorphism groups of 2-(v, k, 1) (k=6, 7, 8, 9) designs

被引：0
|
作者：
Han, Guangguo [1 ]
机构：
[1] Hangzhou Dianzi Univ, Inst Math, Hangzhou 310018, Zhejiang, Peoples R China
来源：
DISCRETE MATHEMATICS | 2008年 / 308卷 / 23期
基金：
中国国家自然科学基金;
关键词：
Block design; Block transitive; Automorphism group; Unsolvable group;
D O I：
10.1016/j.disc.2007.10.051
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study block transitive automorphism groups of 2-(v, k, 1) block designs. Let D be a 2-(v, k, 1) (k = 6, 7, 8, 9) design admitting a block transitive, point primitive but not flag transitive group G of automorphisms. We prove that if G is unsolvable, then G does not admit an exceptional simple group of Lie type as its socle. Moreover, for a 2-(v, 9, 1) design, we also prove that there does not exist any block transitive, point imprimitive, unsolvable group G of automorphisms. (C) 2007 Elsevier B.V. All rights reserved.
引用
收藏
页码：5632 / 5644
页数：13
相关论文
共 50 条
  • [1] Unsolvable Block-Transitive Automorphism Groups of 2-(v, 31, 1) Designs
    Li, Shangzhao
    Dai, Shaojun
    Jiang, Liyuan
    ARS COMBINATORIA, 2014, 117 : 469 - 476
  • [2] Unsolvable block transitive automorphism groups of 2-(v,5,1) designs
    Han, Guangguo
    Li, Huiling
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 2007, 114 (01) : 77 - 96
  • [3] Unsolvable Block Transitive Automorphism Groups of 2-(v,11,1) Designs
    Liao, Xiaolian
    Chen, Guohua
    He, Peiling
    JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, 2014, 17 (5-6): : 511 - 527
  • [4] BLOCK TRANSITIVE AUTOMORPHISM-GROUPS OF 2-(V,K,1) BLOCK-DESIGNS
    CAMINA, A
    SIEMONS, J
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 1989, 51 (02) : 268 - 276
  • [5] Solvable block-transitive automorphism groups of 2-(v, k, 1) designs
    Li, HL
    Liu, WJ
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 2001, 93 (01) : 182 - 191
  • [6] Block-transitive automorphism groups of 2-( v , k , λ ) $(v,k,\lambda )$ designs with ( r , k ) = 1 $(r,k)=1$
    Zhang, Wanbao
    Zhou, Shenglin
    JOURNAL OF COMBINATORIAL DESIGNS, 2022, 30 (05) : 315 - 331
  • [7] Reduction of flag-transitive automorphism groups of 2-(v, k, λ) designs with (r -λ, k)=1
    Zhang, Wanbao
    Zhou, Shenglin
    DISCRETE MATHEMATICS, 2021, 344 (10)
  • [8] Block-Transitive 2-（v,k,1） Designs and Groups E6（q）
    Guang Guo HAN1
    2. Institute of Information Engineering
    Journal of Mathematical Research with Applications, 2010, (04) : 581 - 588
  • [9] The 2-(v, 13, 1) designs with block transitive automorphism
    Dai, Shaojun
    Zhang, Ruihai
    ARS COMBINATORIA, 2013, 110 : 15 - 21
  • [10] Block transitive 2-(v, k, 1) designs and PGL2(q) groups
    Tang, Jianxiong
    Yang, Chaohui
    Li, Shangzhao
    Dai, Shaojun
    Liu, Weijun
    APPLIED MATHEMATICS AND COMPUTATION, 2020, 374
12345