具有点传递自同构群的2-(196,6,1)设计的不存在性

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2026-09-07 Epub Date: 2026-07-31 DOI:10.1002/jcd.70029

Xiaohong Zhang, Shenglin Zhou

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引用次数: 0

摘要

Camina和Di Martino证明了任何2-(196,6,1)设计的块传递自同构群必须是标志传递的。然而，对于这样的设计，点传递自同构群是否存在的问题仍然没有解决。在本研究中，我们证明了no 2-(196,6,1)设计允许一个点传递自同构群。

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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Nonexistence of a 2- ( 196 , 6 , 1 ) Design With a Point-Transitive Automorphism Group

Camina and Di Martino proved that any block-transitive automorphism group of a 2- $(196, 6, 1)$ design must be flag-transitive. However, the question whether a point-transitive automorphism group can exist for such a design remains unsolved. In the present study, we show that no 2- $(196, 6, 1)$ design admits a point-transitive automorphism group.

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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.