3-(v,7,λ)设计上的区传递自同构群  

Block-transitive Automorphism Groups of 3-(v,7,λ)Designs

作　　者：陈诗涵 代少军 赵坤[2] Chen Shihan;Dai Shaojun;Zhao Kun(School of Mathematical Sciences,Tiangong University,Tianjin 300387,China;School of Science,Jiamusi University,Jiamusi 154007,China)

机构地区：[1]天津工业大学数学科学学院,天津300387 [2]佳木斯大学理学院,佳木斯154007

出　　处：《数学理论与应用》2024年第2期80-91,共12页Mathematical Theory and Applications

基　　金：supported by the National Natural Science Foundation of China(Nos.12371335,12071484);Hunan Provincial Natural Science Foundation(No.2020JJ4675);Scientific Research Fund of Heilongjiang Provincial Education Department(No.22KYYWF0594);College Students’Innovation and Entrepreneurship Training Program(school-level project,No.202310058177)。

摘　　要：设S=(P,B)是一个非平凡的3-(v,7,λ)设计且满足λ≥2.本文证明:如果G是S上的一个区传递自同构群,则G是仿射型或者几乎单型的点本原群.此外,我们还考虑G的基柱为交错群A_n的一种有限几乎单群的情形.Let S=(P,B)be a nontrivial 3-(v,7,λ)design withλ≥2.In this paper we show that if G is a block-transitive automorphism group of S,then G is point-primitive of affine or almost simple type.In addition,the case that G is a finite almost simple group with an alternating group socle A_n is considered as well.

关 键 词：自同构群 区传递 3-设计 

分 类 号：O152[理学—数学]