{"title":"λ≥(r,λ)2的2-设计的旗跨自形群不是积型的","authors":"Huiling Li , Zhilin Zhang , Shenglin Zhou","doi":"10.1016/j.jcta.2024.105923","DOIUrl":null,"url":null,"abstract":"<div><p>In this note we show that a flag-transitive automorphism group <em>G</em> of a non-trivial 2-<span><math><mo>(</mo><mi>v</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>λ</mi><mo>)</mo></math></span> design with <span><math><mi>λ</mi><mo>≥</mo><msup><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>λ</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> is not of product action type. In conclusion, <em>G</em> is a primitive group of affine or almost simple type.</p></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"208 ","pages":"Article 105923"},"PeriodicalIF":0.9000,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Flag-transitive automorphism groups of 2-designs with λ ≥ (r,λ)2 are not product type\",\"authors\":\"Huiling Li , Zhilin Zhang , Shenglin Zhou\",\"doi\":\"10.1016/j.jcta.2024.105923\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this note we show that a flag-transitive automorphism group <em>G</em> of a non-trivial 2-<span><math><mo>(</mo><mi>v</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>λ</mi><mo>)</mo></math></span> design with <span><math><mi>λ</mi><mo>≥</mo><msup><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>λ</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> is not of product action type. In conclusion, <em>G</em> is a primitive group of affine or almost simple type.</p></div>\",\"PeriodicalId\":50230,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series A\",\"volume\":\"208 \",\"pages\":\"Article 105923\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-06-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory Series A\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0097316524000621\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series A","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0097316524000621","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
在本注释中,我们证明了一个非三维 2-(v,k,λ) 设计的、λ≥(r,λ)2 的旗反自形群 G 不属于积作用类型。总之,G 是仿射型或近似简单型的基元群。
Flag-transitive automorphism groups of 2-designs with λ ≥ (r,λ)2 are not product type
In this note we show that a flag-transitive automorphism group G of a non-trivial 2- design with is not of product action type. In conclusion, G is a primitive group of affine or almost simple type.
期刊介绍:
The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.