{"title":"有限生成无扭转幂零群的矩阵表示的维数","authors":"Maggie E. Habeeb, Delaram Kahrobaei","doi":"10.1515/gcc-2013-0011","DOIUrl":null,"url":null,"abstract":"Abstract. It is well known that any polycyclic group, and hence any finitely generated nilpotent group, can be embedded into for an appropriate ; that is, each element in the group has a unique matrix representation. An algorithm to determine this embedding was presented in [J. Algebra 300 (2006), 376–383]. In this paper, we determine the complexity of the crux of the algorithm and the dimension of the matrices produced as well as provide a modification of the algorithm presented in [J. Algebra 300 (2006), 376–383].","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"47 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On the dimension of matrix representations of finitely generated torsion free nilpotent groups\",\"authors\":\"Maggie E. Habeeb, Delaram Kahrobaei\",\"doi\":\"10.1515/gcc-2013-0011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. It is well known that any polycyclic group, and hence any finitely generated nilpotent group, can be embedded into for an appropriate ; that is, each element in the group has a unique matrix representation. An algorithm to determine this embedding was presented in [J. Algebra 300 (2006), 376–383]. In this paper, we determine the complexity of the crux of the algorithm and the dimension of the matrices produced as well as provide a modification of the algorithm presented in [J. Algebra 300 (2006), 376–383].\",\"PeriodicalId\":119576,\"journal\":{\"name\":\"Groups Complex. Cryptol.\",\"volume\":\"47 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Groups Complex. Cryptol.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/gcc-2013-0011\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Complex. Cryptol.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/gcc-2013-0011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the dimension of matrix representations of finitely generated torsion free nilpotent groups
Abstract. It is well known that any polycyclic group, and hence any finitely generated nilpotent group, can be embedded into for an appropriate ; that is, each element in the group has a unique matrix representation. An algorithm to determine this embedding was presented in [J. Algebra 300 (2006), 376–383]. In this paper, we determine the complexity of the crux of the algorithm and the dimension of the matrices produced as well as provide a modification of the algorithm presented in [J. Algebra 300 (2006), 376–383].
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