{"title":"关于Hilbert 2类场塔的注记","authors":"A. Azizi, M. M. Chems-Eddin, A. Zekhnini","doi":"10.21136/mb.2022.0056-21","DOIUrl":null,"url":null,"abstract":"Let k be a number field with a 2-class group isomorphic to the Klein fourgroup. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields k = Q ( √ d, √ −1 ) , which leads to a correction of some parts in the main results of A.Azizi and A. Zekhini (2020).","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Note on the Hilbert 2-class field tower\",\"authors\":\"A. Azizi, M. M. Chems-Eddin, A. Zekhnini\",\"doi\":\"10.21136/mb.2022.0056-21\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let k be a number field with a 2-class group isomorphic to the Klein fourgroup. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields k = Q ( √ d, √ −1 ) , which leads to a correction of some parts in the main results of A.Azizi and A. Zekhini (2020).\",\"PeriodicalId\":45392,\"journal\":{\"name\":\"Mathematica Bohemica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-01-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica Bohemica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21136/mb.2022.0056-21\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Bohemica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21136/mb.2022.0056-21","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Let k be a number field with a 2-class group isomorphic to the Klein fourgroup. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields k = Q ( √ d, √ −1 ) , which leads to a correction of some parts in the main results of A.Azizi and A. Zekhini (2020).
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