{"title":"无边群中的公共横截面和补集","authors":"","doi":"10.1007/s10801-024-01299-x","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>Given a finite abelian group <em>G</em> and cyclic subgroups <em>A</em>, <em>B</em>, <em>C</em> of <em>G</em> of the same order, we find necessary and sufficient conditions for <em>A</em>, <em>B</em>, <em>C</em> to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups, we give a sufficient criterion when there exists a common complement. Moreover, in several cases where a common transversal exists, we provide concrete constructions. </p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Common transversals and complements in abelian groups\",\"authors\":\"\",\"doi\":\"10.1007/s10801-024-01299-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3>Abstract</h3> <p>Given a finite abelian group <em>G</em> and cyclic subgroups <em>A</em>, <em>B</em>, <em>C</em> of <em>G</em> of the same order, we find necessary and sufficient conditions for <em>A</em>, <em>B</em>, <em>C</em> to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups, we give a sufficient criterion when there exists a common complement. Moreover, in several cases where a common transversal exists, we provide concrete constructions. </p>\",\"PeriodicalId\":14926,\"journal\":{\"name\":\"Journal of Algebraic Combinatorics\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-02-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebraic Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10801-024-01299-x\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10801-024-01299-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
摘要 给定一个有限无秩群 G 和 G 的同阶循环子群 A、B、C，我们发现 A、B、C 的余集有必要条件和充分条件。对于任意数量的循环子群，我们给出了存在共同补集的充分条件。此外，在存在共同横截面的几种情况下，我们提供了具体的构造。
Common transversals and complements in abelian groups
Abstract
Given a finite abelian group G and cyclic subgroups A, B, C of G of the same order, we find necessary and sufficient conditions for A, B, C to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups, we give a sufficient criterion when there exists a common complement. Moreover, in several cases where a common transversal exists, we provide concrete constructions.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
