On symmetric designs with flag-transitive and point-quasiprimitive automorphism groups

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2023-11-05 DOI:10.1002/jcd.21924

Zhilin Zhang, Jianfu Chen, Shenglin Zhou

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引用次数: 0

Abstract

Let $D = (P, ℬ)$ be a nontrivial symmetric $(v, k, λ)$ -design with $λ \leq 100$ , and let $G$ be a flag-transitive automorphism group of $D$ . In this paper, we show that if $G$ is quasiprimitive on $P$ , then $G$ is of holomorph affine or almost simple type. Moreover, if $G$ is imprimitive on $P$ , then $G$ is of almost simple type. According to this observation and to the classification of the finite simple groups we determine all such symmetric designs and the corresponding automorphism groups. We conclude with two open problems and a conjecture.

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关于具有旗变换群和点准三态群的对称设计

设 D = ( P , ℬ ) 是一个非对称对称 ( v , k , λ ) 设计，且 λ ≤ 100 。 -设计，且 λ ≤ 100 ，设 G 是 D 的旗反自变群。本文将证明，如果 G 在 P 上是类对立的，那么 G 是全形仿射型或近似简单型。此外，如果 G 在 P 上是隐含的，那么 G 几乎是简单类型的。根据这一观察和有限简单群的分类，我们确定了所有这类对称设计和相应的自变群。最后，我们提出两个悬而未决的问题和一个猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.