{"title":"整体域上除法代数的约简范数1群","authors":"G. Tomanov","doi":"10.1070/IM1992V039N01ABEH002231","DOIUrl":null,"url":null,"abstract":"It is proved that if the Platonov-Margulis conjecture on the standard structure of normal subgroups holds for the division algebras of index r, then it also holds for the division algebras of index n=2mr, for any m. Thus the conjecture is proved for the division algebras of index n=2m, for any m, and its proof in the general case is reduced to the case of division algebras of odd index.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"39 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"ON THE REDUCED NORM 1 GROUP OF A DIVISION ALGEBRA OVER A GLOBAL FIELD\",\"authors\":\"G. Tomanov\",\"doi\":\"10.1070/IM1992V039N01ABEH002231\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is proved that if the Platonov-Margulis conjecture on the standard structure of normal subgroups holds for the division algebras of index r, then it also holds for the division algebras of index n=2mr, for any m. Thus the conjecture is proved for the division algebras of index n=2m, for any m, and its proof in the general case is reduced to the case of division algebras of odd index.\",\"PeriodicalId\":159459,\"journal\":{\"name\":\"Mathematics of The Ussr-izvestiya\",\"volume\":\"39 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-izvestiya\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/IM1992V039N01ABEH002231\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-izvestiya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/IM1992V039N01ABEH002231","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ON THE REDUCED NORM 1 GROUP OF A DIVISION ALGEBRA OVER A GLOBAL FIELD
It is proved that if the Platonov-Margulis conjecture on the standard structure of normal subgroups holds for the division algebras of index r, then it also holds for the division algebras of index n=2mr, for any m. Thus the conjecture is proved for the division algebras of index n=2m, for any m, and its proof in the general case is reduced to the case of division algebras of odd index.
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