On Flag-Transitive 2- ( v , k , λ ) Designs With λ ≤ 4

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2026-10-12 Epub Date: 2026-08-28 DOI:10.1002/jcd.70033

Yihui Li, Shenglin Zhou

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引用次数: 0

Abstract

Let $D$ be a non-trivial 2- $(v, k, λ)$ design with $λ \leq 4$ , admitting a flag-transitive automorphism group $G$ which is also properly innately transitive on points. Then $G$ is of almost simple quotient type. As a corollary, we obtain that $G$ is innately transitive on points if and only if it is primitive when $λ \leq 3$ . And we proved that there exists a unique 2- $(v, k, λ)$ design for $λ = 4$ with a automorphism group $G$ acting transitively on flags and properly innately transitively on points, that is, the unique symmetric 2- $(15, 8, 4)$ design with $G ≅ Γ L_{2} (4)$ and its plinth $K ≅ A_{5}$ as in [14, Proposition 1.5].

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λ≤4的flag -传递2- (v, k, λ)设计

设D是非平凡的2- (v)k ,λ)设计λ≤4；承认一个标志-传递自同构群G，它也是在点上固有传递的。则G是几乎单商型。作为推论，我们得到当且仅当λ≤3时G是本原的，它在点上是固有可传递的。我们证明了存在唯一的2- （v, k,）具有自同构群的λ = 4的λ)设计G传递作用于标志上，并固有地传递作用于点上，即唯一对称的2- （15）8 ,4)设计用G = Γ l2(4)及其基座K = A参见[14，提案1.5]。

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来源期刊

Journal of Combinatorial Designs 数学-数学

CiteScore

1.60

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Combinatorial Designs is an international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory. All topics in design theory, and in which design theory has important applications, are covered, including: block designs, t-designs, pairwise balanced designs and group divisible designs Latin squares, quasigroups, and related algebras computational methods in design theory construction methods applications in computer science, experimental design theory, and coding theory graph decompositions, factorizations, and design-theoretic techniques in graph theory and extremal combinatorics finite geometry and its relation with design theory. algebraic aspects of design theory. Researchers and scientists can depend on the Journal of Combinatorial Designs for the most recent developments in this rapidly growing field, and to provide a forum for both theoretical research and applications. All papers appearing in the Journal of Combinatorial Designs are carefully peer refereed.