Block-transitive 3-(v, k, 1) designs on exceptional groups of Lie type

IF 0.6 3区数学 Q3 MATHEMATICS Journal of Algebraic Combinatorics Pub Date : 2024-04-06 DOI:10.1007/s10801-024-01315-0

引用次数: 0

Abstract

Let ${\mathcal {D}}$ be a non-trivial G-block-transitive 3-(v, k, 1) design, where $T\le G \le \textrm{Aut}(T)$ for some finite non-abelian simple group T. It is proved that if T is a simple exceptional group of Lie type, then T is either the Suzuki group ${}^2B_2(q)$ or $G_2(q)$ . Furthermore, if $T={}^2B_2(q)$ then the design ${\mathcal {D}}$ has parameters $v=q^2+1$ and $k=q+1$ , and so ${\mathcal {D}}$ is an inverse plane of order q, and if $T=G_2(q)$ then the point stabilizer in T is either $\textrm{SL}_3(q).2$ or $\textrm{SU}_3(q).2$ , and the parameter k satisfies very restricted conditions.

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李型异常群上的块传递 3-(v, k, 1) 设计

摘要让 ${mathcal {D}}$ 是一个非难的 G 块传递的 3-(v,k,1)设计，其中 $T\le G \le \textrm{Aut}(T)$ 对于某个有限的非阿贝尔简单群 T。此外，如果 $T={}^2B_2(q)$ 那么设计 ${\mathcal {D}}$ 有参数 $v=q^2+1$ 和 $k=q+1$ ，所以 ${\mathcal {D}}$ 是一个 q 阶的反平面，如果 $T=G_2(q)$ 那么 T 中的点稳定器要么是 \(\textrm{SL}_3(q).2) 或者（textrm{SU}_3(q).参数 k 满足非常有限的条件。

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 Algebraic Combinatorics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics. The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.

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