{"title":"On central digraphs constructed from left loops and loops","authors":"Rajaram Rawat","doi":"10.56415/qrs.v31.09","DOIUrl":null,"url":null,"abstract":"Let An be the set of n X n zero-one matrices satisfying the matrix equation A2 = Jn; where Jn is n X n matrices of all ones. In this article, it is proved that the number of non-isomorphic left loops of order k gives the lower bound to the size of An for n = k2. Mainly we have established that any matrix in An corresponding to loop has rank 2k - 2, where n = k2, for some positive integer k.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quasigroups and Related Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56415/qrs.v31.09","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
Let An be the set of n X n zero-one matrices satisfying the matrix equation A2 = Jn; where Jn is n X n matrices of all ones. In this article, it is proved that the number of non-isomorphic left loops of order k gives the lower bound to the size of An for n = k2. Mainly we have established that any matrix in An corresponding to loop has rank 2k - 2, where n = k2, for some positive integer k.