交错群与旗传递$2-(v,k,4)$对称设计[EB/OL]
北京：中国科技论文在线
2、 Department of Mathematics, South China University of Technology, GuangZhou 510640
证明了如果旗传递点本原的2-(v,k,4) 对称设计D的自同构群G的基柱为交错群An,其中n>=5, 则(v,k)=(15,8)且设计D=(P,B)是下列之一:(i) P为V4(2)的一维子空间的集合, B 为PX的子集族, 这里X是包含在V4(2)的超平面里的一维子空间的集合,G=A7或者A8, 且点稳定化子分别为Gx=L3(2) 或AGL3(2)
(ii) P为Ω6: ={1,2,
, 6}的2-子集的集合, B为PX的子集族, 这里 X={Y}U{Z是Ω6的2-子集}Z∩Y=θ}, 其中Y是Ω6的2-子集,G=A6 或者 S6, 且点稳定化子分别为 Gx=S4 或 S4*Z2
关键词： 群论
ZHOU Shenglin 2,* （ 1、 Department of Mathematics, South China University of Technology, GuangZhou 510640
） 摘要： 本文研究旗传递的2-(v,k,4)对称设计的分类
） Abstract： In this paper, we study the classification offlag-transitive, point-primitive 2-(v,k,4) symmetric designs
Weprove that if the socle of the automorphism group of aflag-transitive, point-primitive nontrivial2-(v,k,4) symmetric design D is an alternating group An for n>=5, then (v,k)=(15,8) and D=(P,B) is one of the following:(i) P is the set of one-dimensional subspaces of V4(2), B is acollection of PX, where X is the set of one-dimensional subspacescontained in one hyperplane of V4(2), G=A7 or A8, andthe stabiliser Gx=L3(2) or AGL3(2) respectively
(ii) P is the set of 2- of Ω6: ={1,2,
, 6}, B is a collection ofPX, where X is Y{Y}U{Z is a 2- of Ω6 Z∩Y=θ}, Y is a 2- of Ω6, G=A6 or S6, and Gx=S4 or S4*Z2 respectively
Keywords： Group theory; Automorphism group; Alternating group 下载PDF阅读器 PDF全文下载： 初稿 （ 112 ） 原始数据 作者简介： Dong Huili,(1981-),female,Ph
D
student,major research direction:groups and designs
通信联系人： Zhou Shenglin,(1968-),male,professor,major research direction:group and design theory
【收录情况】 中国科技论文在线： 董会莉
