{"title":"有限阿贝尔群的非全秩因子分解","authors":"K. Amin","doi":"10.4236/OJDM.2017.72005","DOIUrl":null,"url":null,"abstract":"Tilings of p-groups are closely associated with error-correcting codes. In [1], M. Dinitz, attempting to generalize full-rank tilings of Zn2 to arbitrary finite abelian groups, was able to show that if p ≥5, then Znp admits full-rank tiling and left the case p=3, as an open question. The result proved in this paper the settles of the question for the case p=3.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"07 1","pages":"720-726"},"PeriodicalIF":0.0000,"publicationDate":"2017-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-Full Rank Factorization of Finite Abelian Groups\",\"authors\":\"K. Amin\",\"doi\":\"10.4236/OJDM.2017.72005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Tilings of p-groups are closely associated with error-correcting codes. In [1], M. Dinitz, attempting to generalize full-rank tilings of Zn2 to arbitrary finite abelian groups, was able to show that if p ≥5, then Znp admits full-rank tiling and left the case p=3, as an open question. The result proved in this paper the settles of the question for the case p=3.\",\"PeriodicalId\":61712,\"journal\":{\"name\":\"离散数学期刊(英文)\",\"volume\":\"07 1\",\"pages\":\"720-726\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-04-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"离散数学期刊(英文)\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://doi.org/10.4236/OJDM.2017.72005\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"离散数学期刊(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/OJDM.2017.72005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Non-Full Rank Factorization of Finite Abelian Groups
Tilings of p-groups are closely associated with error-correcting codes. In [1], M. Dinitz, attempting to generalize full-rank tilings of Zn2 to arbitrary finite abelian groups, was able to show that if p ≥5, then Znp admits full-rank tiling and left the case p=3, as an open question. The result proved in this paper the settles of the question for the case p=3.
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