{"title":"六阶半群的有限基问题","authors":"Edmond W. H. Lee, Wen Ting Zhang","doi":"10.1112/S1461157014000412","DOIUrl":null,"url":null,"abstract":"Two semigroups are distinct if they are neither isomorphic nor anti-isomorphic. Although there exist $15\\,973$ pairwise distinct semigroups of order six, only four are known to be non-finitely based. In the present article, the finite basis property of the other $15\\,969$ distinct semigroups of order six is verified. Since all semigroups of order five or less are finitely based, the four known non-finitely based semigroups of order six are the only examples of minimal order.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"18 1","pages":"1-129"},"PeriodicalIF":0.0000,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157014000412","citationCount":"24","resultStr":"{\"title\":\"Finite Basis Problem for Semigroups of Order Six\",\"authors\":\"Edmond W. H. Lee, Wen Ting Zhang\",\"doi\":\"10.1112/S1461157014000412\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Two semigroups are distinct if they are neither isomorphic nor anti-isomorphic. Although there exist $15\\\\,973$ pairwise distinct semigroups of order six, only four are known to be non-finitely based. In the present article, the finite basis property of the other $15\\\\,969$ distinct semigroups of order six is verified. Since all semigroups of order five or less are finitely based, the four known non-finitely based semigroups of order six are the only examples of minimal order.\",\"PeriodicalId\":54381,\"journal\":{\"name\":\"Lms Journal of Computation and Mathematics\",\"volume\":\"18 1\",\"pages\":\"1-129\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1112/S1461157014000412\",\"citationCount\":\"24\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lms Journal of Computation and Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1112/S1461157014000412\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lms Journal of Computation and Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1112/S1461157014000412","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Two semigroups are distinct if they are neither isomorphic nor anti-isomorphic. Although there exist $15\,973$ pairwise distinct semigroups of order six, only four are known to be non-finitely based. In the present article, the finite basis property of the other $15\,969$ distinct semigroups of order six is verified. Since all semigroups of order five or less are finitely based, the four known non-finitely based semigroups of order six are the only examples of minimal order.
期刊介绍：
LMS Journal of Computation and Mathematics has ceased publication. Its final volume is Volume 20 (2017). LMS Journal of Computation and Mathematics is an electronic-only resource that comprises papers on the computational aspects of mathematics, mathematical aspects of computation, and papers in mathematics which benefit from having been published electronically. The journal is refereed to the same high standard as the established LMS journals, and carries a commitment from the LMS to keep it archived into the indefinite future. Access is free until further notice.
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