{"id":2428,"date":"2024-11-04T14:04:03","date_gmt":"2024-11-04T14:04:03","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2428"},"modified":"2024-11-08T08:18:18","modified_gmt":"2024-11-08T08:18:18","slug":"arithmetic-of-some-real-triquadratic-fields-units-and-2-class-groups","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/arithmetic-of-some-real-triquadratic-fields-units-and-2-class-groups\/","title":{"rendered":"Arithmetic of some real triquadratic fields; Units and 2-class groups"},"content":{"rendered":"\n
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Moroccan Journal of Algebra and Geometry with Applications<\/strong><\/p>\n\n\n\n

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Arithmetic of some real triquadratic fields; Units and 2-class groups<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Mohamed Mahmoud Chems-Eddin <\/strong><\/i>
Departement of Mathematics, Faculty of Sciences Dhar El Mahraz,
Sidi Mohamed Ben Abdellah University, Fez, Morocco<\/p>\n\n\n\n

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Pages 358\u2013387 | Received 28 March 2024, Accepted 23 July 2024, Published 08 November 2024 <\/span><\/p>\n\n\n\n

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Abstract<\/span><\/strong><\/p>\n\n\n\n

In this paper, we compute the unit groups and the 2-class numbers of the Fr\u00f6hlich’s triquadratic fields \\mathbb{K}=\\mathbb{Q}(\\sqrt{2},\\sqrt{p},\\sqrt{q})<\/span>, where p<\/span> and q<\/span> are two prime numbers such that (p\\equiv 1 \\pmod 8<\/span> and q\\equiv 3 \\pmod 4<\/span>) or (p\\equiv 5<\/span> or 3 \\pmod 8<\/span> and q\\equiv 3 \\pmod 4<\/span>). Furthermore, we determine some families of the fields \\mathbb{K}<\/span> whose 2-class groups are trivial or cyclic non trivial, and some other families with 2-class groups isomorphic to the Klein group.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/span>  Real multiquadratic fields, unit group, 2-class group, 2-class number.<\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> 11R04, 11R27, 11R29, 11R37.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles Arithmetic of some real triquadratic fields; Units and 2-class groups Mohamed Mahmoud Chems-Eddin Departement of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco Pages 358\u2013387 | Received 28 March 2024, Accepted 23 July 2024, Published 08 November 2024 Abstract Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-page-builder.php","meta":{"footnotes":""},"class_list":["post-2428","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2428","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/comments?post=2428"}],"version-history":[{"count":7,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2428\/revisions"}],"predecessor-version":[{"id":2515,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2428\/revisions\/2515"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2428"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}