{"title":"2-adic cofiltration of SO3(Q)","authors":"Tengiz Bokelavadze , Raffaello Caserta","doi":"10.1016/j.trmi.2017.06.001","DOIUrl":null,"url":null,"abstract":"<div><p>We prove that the group <span><math><msub><mrow><mi>SO</mi></mrow><mrow><mn>3</mn></mrow></msub><mrow><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></math></span> of rational rotations is the inverse limit of a family of finite solvable groups of order <span><math><msup><mrow><mn>2</mn></mrow><mrow><mn>3</mn><mi>k</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>⋅</mo><mn>3</mn></math></span>, whose <span><math><mn>2</mn></math></span>-Sylow subgroups have nilpotency class <span><math><mn>2</mn><mi>k</mi><mo>−</mo><mn>3</mn></math></span>, exponent <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span>, and Frattini subgroups coinciding with the commutator subgroups, and we give generators for these groups.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"171 3","pages":"Pages 257-263"},"PeriodicalIF":0.3000,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.06.001","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of A Razmadze Mathematical Institute","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2346809217300077","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that the group of rational rotations is the inverse limit of a family of finite solvable groups of order , whose -Sylow subgroups have nilpotency class , exponent , and Frattini subgroups coinciding with the commutator subgroups, and we give generators for these groups.