交替群与点数为平方的点基元线性空间

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2023-02-26 DOI:10.1002/jcd.21879

Haiyan Guan, Shenglin Zhou

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引用次数: 0

摘要

本文对点基元有限正则线性空间的分类作了进一步的贡献。设S$｛\mathscr｛S｝｝$是一个非平凡的有限正则线性空间，其点数v$v$为平方。我们证明了如果G≤Aut（S）$G\le\text｛Aut｝（｛\mathscr｛S｝｝）$是具有交替socle的点基元，则S$｛\mathscr｛S｝｝$是投影空间PG（3，2）$\text｛PG｝（3,2）$。

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Alternating groups and point-primitive linear spaces with number of points being squarefree

This paper is a further contribution to the classification of point-primitive finite regular linear spaces. Let $S$ be a nontrivial finite regular linear space whose number of points $v$ is squarefree. We prove that if $G \leq Aut (S)$ is point-primitive with an alternating socle, then $S$ is the projective space $PG (3, 2)$ .

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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.