On the automorphisms of designs

详细信息    查看全文

• 作者：Shangzhao Li ; ^a ; ^b ; ^{lszfd2004@126.com" class="auth_mail" title="E-mail the corresponding author} ; Weijun Liu^c ; Xianhua Li^b
• 关键词：Block-transitive ; DD design ; Automorphism ; Socle
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：292
• 期：Complete
• 页码：120-127
• 全文大小：378 K

文摘

Thirty years ago, a six-person team classified the pairs (D,G)$(\mathcal{D},G)$ where D$\mathcal{D}$ is a 9a25b33e8aff1c8466cfb909d224f" title="Click to view the MathML source">2−(v,k,1)$2-(v,k,1)$ design and G   is a flag-transitive automorphism group of 8b" title="Click to view the MathML source">D,$\mathcal{D},$ with the exception of those in which G   is a one-dimensional affine group. Since then the effort has been to classify those 9a25b33e8aff1c8466cfb909d224f" title="Click to view the MathML source">D,$\mathcal{D},$ designs which are block-transitive but not flag-transitive. This paper contributes to the program for determining the pairs 2−(v,k,1)$2-(v,k,1)$ in which (D,G)$(\mathcal{D},G)$ has a block-transitive group G   of automorphisms. It is clear that if one wishes to study the structure of a finite group acting on a 9a25b33e8aff1c8466cfb909d224f" title="Click to view the MathML source">D$\mathcal{D}$ design then describing the socle is an important first step. Here we prove that if G   is a block-transitive group of automorphisms of 2−(v,k,1)$2-(v,k,1)$ which has 8b656d7e2ab4e7ddee9662350d" title="Click to view the MathML source">D$\mathcal{D}$ as its socle then T   is also transitive on the blocks of T=²F₄(q)$T={}^2{F}_4\left(q\right)$.