{"title":"离散初等群","authors":"Zhou Qing","doi":"10.1360/YA1993-36-9-1047","DOIUrl":null,"url":null,"abstract":"This paper discusses discrete elementary subgroups in the Mobius group M( R n ).With a help of geometry,it is proved that these groups are isomorphic to either a group extension of Z by a finite subgroup of SO ( n ) or an extension of a finite group by a free Abelian group of rank k ≤ n .","PeriodicalId":256661,"journal":{"name":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"The Discrete Elementary Groups\",\"authors\":\"Zhou Qing\",\"doi\":\"10.1360/YA1993-36-9-1047\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper discusses discrete elementary subgroups in the Mobius group M( R n ).With a help of geometry,it is proved that these groups are isomorphic to either a group extension of Z by a finite subgroup of SO ( n ) or an extension of a finite group by a free Abelian group of rank k ≤ n .\",\"PeriodicalId\":256661,\"journal\":{\"name\":\"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-09-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1360/YA1993-36-9-1047\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1360/YA1993-36-9-1047","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper discusses discrete elementary subgroups in the Mobius group M( R n ).With a help of geometry,it is proved that these groups are isomorphic to either a group extension of Z by a finite subgroup of SO ( n ) or an extension of a finite group by a free Abelian group of rank k ≤ n .
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