Suzuki群与旗传递点本原2-（ν，Κ，λ）设计
Suzuki Group and Flag-Transitive Point-Primitive 2-（ν，Κ，λ）Designs
DOI: 10.12677/PM.2019.92022, PDF,    科研立项经费支持
作者: 王雨洁：华南理工大学数学学院，广东 广州
关键词: 2-设计；旗传递；Suzuki群；2-Design； Flag-Transitive； Suzuki Group
摘要: 群论与组合设计有着紧密的内在关系，主要通过设计的自同构群的旗传递性、点本原性等性质来体现。本文研究D是一个非平凡的2-（ν，Κ，λ）设计，其中λ≤10。若G≤Aut(D)是旗传递、点本原的群，且G=Sz(q)，则D是一个2-(65, 8, 7)设计，且G=Sz(8)。
Abstract: There are important internal connections between groups and combinatorial designs, which re-flected by the flag-transitivity, point-primitivity or other properties of the automorphism groups. Let D be non-trivial 2-designs with λ≤10. Assume that G=Sz(q) is a flag-transitive point-primitive automorphism group of D . Then D  is a 2-(65, 8, 7) design and G=Sz(8) .
文章引用：王雨洁. Suzuki群与旗传递点本原2-（ν，Κ，λ）设计[J]. 理论数学, 2019, 9(2): 174-181. https://doi.org/10.12677/PM.2019.92022

参考文献

[1] Zieschang, P.-H. (1988) Flag-Transitive Automorphism Groups of 2-Designs with (γ, λ) = 1. Journal of Algebra, 118, 265-275.
[Google Scholar] [CrossRef] 
[2] Regueiro, E.O. (2005) On Primitive and Reduction for Flag-Transitive Symmetric Designs. Journal of Combinatorial Theory, Series A, 109, 135-148.
[Google Scholar] [CrossRef] 
[3] Regueiro, E.O. (2010) Reduction for Primitive Flag-Transitive (v, k, 4)-Symmetric Designs. Designs, Codes and Cryptography, 56, 61-63.
[Google Scholar] [CrossRef] 
[4] Fang, W.D., Dong, H.L. and Zhou, S.L. (2010) Flag-Transitive 2-(v, k, 4) Symmetric Designs. Ars Combinatoria, 95, 333-342.
[5] Tian, D.L. and Zhou, S.L. (2013) Flag-Transitive Point-Primitive Symmetric (v, k, λ) Designs with λ at Most 100. Journal of Combinatorial Designs, 21, 127-141.
[Google Scholar] [CrossRef] 
[6] Liang, H.X. and Zhou, S.L. (2016) Flag-Transitive Point-Primitive Automorphism Groups of Nonsymmetric 2-(v, k, 2) Designs. Journal of Combinatorial Designs, 24, 421-435.
[Google Scholar] [CrossRef] 
[7] Ionin, Y.J. and van Trung, T. (2007) Symmetric Designs. In: Colbourn, C.J. and Dinitz, J.H., Eds., Handbook of Combinatorial Designs, Chapman Hall/CRC, Boca Raton, 110-124.
[8] Dembowski, P. (1968) Finite Geometries. Springer-Verlag, New York.
[Google Scholar] [CrossRef] 
[9] Davies, H. (1987) Flag-Transitive and Primitivity. Discrete Mathematics, 63, 91-93.
[Google Scholar] [CrossRef] 
[10] Dixon, J.D. and Mortimer, B. (1988) The Primitive Permutation Groups of Degree Less than 1000. Mathematical Proceedings of the Cambridge Philosophical Society, 103, 213-238.
[Google Scholar] [CrossRef] 
[11] Bosma, W., Cannon, J. and Playoust, C. (1997) The MAGMA Algebra System I: The User Language. Journal of Symbolic Computation, 24, 235-265.
[Google Scholar] [CrossRef] 

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