{"title":"局部原始方块设计","authors":"Jianfu Chen, Peice Hua, Cai Heng Li, Yanni Wu","doi":"10.1112/jlms.70221","DOIUrl":null,"url":null,"abstract":"<p>A locally primitive 2-design is a 2-design admitting an automorphism group <span></span><math>\n <semantics>\n <mi>G</mi>\n <annotation>$G$</annotation>\n </semantics></math> with primitive local actions. It is proved that <span></span><math>\n <semantics>\n <mi>G</mi>\n <annotation>$G$</annotation>\n </semantics></math> is point-primitive, and either <span></span><math>\n <semantics>\n <mi>G</mi>\n <annotation>$G$</annotation>\n </semantics></math> is an almost simple group, or <span></span><math>\n <semantics>\n <mi>G</mi>\n <annotation>$G$</annotation>\n </semantics></math> acts on the points as an affine group.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Locally primitive block designs\",\"authors\":\"Jianfu Chen, Peice Hua, Cai Heng Li, Yanni Wu\",\"doi\":\"10.1112/jlms.70221\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A locally primitive 2-design is a 2-design admitting an automorphism group <span></span><math>\\n <semantics>\\n <mi>G</mi>\\n <annotation>$G$</annotation>\\n </semantics></math> with primitive local actions. It is proved that <span></span><math>\\n <semantics>\\n <mi>G</mi>\\n <annotation>$G$</annotation>\\n </semantics></math> is point-primitive, and either <span></span><math>\\n <semantics>\\n <mi>G</mi>\\n <annotation>$G$</annotation>\\n </semantics></math> is an almost simple group, or <span></span><math>\\n <semantics>\\n <mi>G</mi>\\n <annotation>$G$</annotation>\\n </semantics></math> acts on the points as an affine group.</p>\",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":\"112 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2025-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/jlms.70221\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/jlms.70221","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A locally primitive 2-design is a 2-design admitting an automorphism group with primitive local actions. It is proved that is point-primitive, and either is an almost simple group, or acts on the points as an affine group.
期刊介绍:
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.