区传递的2-(v,k,1)设计与射影辛群PSp_n(q)

Block transitive 2-(v,k,1) designs and projective symplectic groups PSp_n(q)

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摘要分类自同构群为射影辛群PSp_n(q)的区传递2-(v,k,1)设计,得到如下定理:设D为一个2-(v,k,1)设计,G≤Aut(D)是区传递,点本原但非旗传递的.若q为偶数且n≥14,则G(?) PSp_n(q). This article is a contribution to the study of the automorphism groups of 2-（v, k, 1） designs. In particular, projective symplectic groups PSpn （q） are studied and the following theorem is proved： Let D be a 2-（v, k, 1） design, G ≤ Aut（D） be block transitive, point primitive but not flat transitive, then G is not PSpn（q）, with q even and n ≥ 14.

作者韩广国方卫东

机构地区杭州电子科技大学数学研究所解放军信息工程大学信息工程学院华南理工大学数学科学学院

出处《高校应用数学学报（A辑）》 CSCD 北大核心 2009年第1期111-120,共10页 Applied Mathematics A Journal of Chinese Universities(Ser.A)

基金国家自然科学基金(10871205)

关键词设计自同构群区传递点本原 design automorphism group block transitive point primitive

分类号 O157.2 [理学—基础数学]

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1Beth T, Jungnickel D, Lenz H. Design Theory[M]. Cambridge: Cambridge University Press, 1986:
2Block R E. On the orbits of collineation groups[J]. Math Z, 1967, 96: 33-49.
3Buekenhout F, Delandtsheer A, Doyen J, et al. Linear spaces with flag-transitive automor- phism groups[J]. Geom Dedicata, 1990, 36: 89-94.
4Camina A R. The scale of automorphism groups of linear spaces[J]. Bull London Math Soc, 1996, 28: 269-272.
5Cantina A R, Spiezia F. Sporadic groups and automorphisms of linear spaces[J]. J Combin Designs, 2000, 8: 353-362.
6Camina A R, Neumann P M, Praeger C E. Alternating groups acting on linear spaces[J]. Proc London Math Soc, 2003, 87: 29-53.
7Liu Weijun. Finite linear spaces admitting a two-dimentional projective linear group[J]. J Combin Theory Ser A, 2003, 103: 209-222.
8Liu Weijun. Finite linear spaces admitting a projective group PSU3(q) with q even[J]. Linear Algebra Appl, 2003, 374: 291-305.
9Spiezia F. Simple groups and automorphisms of linear spaces[D]. Ph D thesis, England: University of East.Anglia, 1997.
10Li Huiling. On block-transitive 2-(v, 4, 1) designs[J]. J Combin Theory Ser A, 1995, 69: 115-124.

二级参考文献14

1方卫东,李慧陵.Camina-Gagen 定理的一个推广[J].数学杂志,1993,13(4):437-442. 被引量：21
2Hughs D R, Piper F C. Design Theory[M]. London: Cambridge University Press, 1986.
3Block R E. On the orbits of collineation groups[J]. Math Z, 1967,96:33-49.
4Buekenhout F,Delandtsheer A,Doyen J, et al. Linear-spaces with flag-transitive automor-phism groups[J]. Geom Dedicata, 1990,36: 89-94.
5Camina A R. The socle of automorphism groups of linear spaces[J]. Bull London Math Soc,1996, 28: 269-272.
6Camina A R, Spiezia F.Sporadic groups and automorphisms of linear spaces[J]. J Combin Designs, 2000,8:353-362.
7Camina A R, Neumann P M, Praeger C E. Alternating groups acting on linear spaces[J].Proc London Math Soc, 2003, 87: 29-53.
8Liu Weijun. Finite linear spaces admitting a two-dimensional projective linear group[J].J Combin Theory Ser A, 2003,103:209-222.
9Liu Weijun. Finite linear spaces admitting a projective group PSU3(q) with q even[J]. Linear Algebra and its Applications, 2003,374:291-305.
10Li Huiling. On block-transitive 2-(u,4,1) designs[J]. J Combin Theory Ser A, 1995, 69: 115-124.

共引文献1

1李上钊.Suzuki群Sz(q)和线性空间的自同构群[J].数学杂志,2016,36(2):298-302.

1刘绍武.域上非正则射影辛群的自同构[J].黑龙江大学自然科学学报,1991,8(4):13-18.
2张良才,聂文敏,张苗,张盟盟.某些射影辛群S_4(q)的OD-刻画[J].西南师范大学学报（自然科学版）,2014,39(12):6-11.

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区传递的2-(v,k,1)设计与射影辛群PSp_n(q)

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