{"title":"域上小阶完全线性群中的参数二分解","authors":"Volodymyr Shchedryk","doi":"10.1007/s11253-024-02323-w","DOIUrl":null,"url":null,"abstract":"<p>We obtain a parametric description of elements of complete linear groups of the second and third orders over an arbitrary field. It is based on their canonical (single-valued) representation as a product of elements from the commutators of certain Jordan matrices and representatives of the left cosets of these groups.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Parametric 2-Decompositions in Complete Linear Groups of Small Order Over a Field\",\"authors\":\"Volodymyr Shchedryk\",\"doi\":\"10.1007/s11253-024-02323-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We obtain a parametric description of elements of complete linear groups of the second and third orders over an arbitrary field. It is based on their canonical (single-valued) representation as a product of elements from the commutators of certain Jordan matrices and representatives of the left cosets of these groups.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11253-024-02323-w\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11253-024-02323-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Parametric 2-Decompositions in Complete Linear Groups of Small Order Over a Field
We obtain a parametric description of elements of complete linear groups of the second and third orders over an arbitrary field. It is based on their canonical (single-valued) representation as a product of elements from the commutators of certain Jordan matrices and representatives of the left cosets of these groups.
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