{"id":1719,"date":"2023-06-14T12:54:44","date_gmt":"2023-06-14T12:54:44","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=1719"},"modified":"2023-10-12T22:03:59","modified_gmt":"2023-10-12T22:03:59","slug":"what-can-we-say-about-the-polya-groupof-a-bicyclic-biquadratic-number-field","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/what-can-we-say-about-the-polya-groupof-a-bicyclic-biquadratic-number-field\/","title":{"rendered":"What can we say about the P\u00f3lya Groupof a Bicyclic Biquadratic Number Field?"},"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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What can we say about the P\u00f3lya Group<\/em><\/strong>
of a Bicyclic Biquadratic Number Field ?<\/em><\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Jean-Luc Chabert <\/strong><\/i>
LAMFA CNRS-UMR 7352, Universit\u00e9 de Picardie, 80039 Amiens, France.<\/p>\n\n\n\n

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Pages 70-82 | Received 21 October 2022, Accepted 13 January 2023, Published 16 June 2023 <\/span><\/p>\n\n\n\n

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

The P\u00f3lya group \\mathcal{P} o(K)<\/span> of a finite Galois extension K<\/span> of \\mathbb{Q}<\/span> is the subgroup of the class group of K<\/span> formed by the strong ambiguous classes of K<\/span>. In this paper, we state a general formula which gives the order of \\mathcal{P} o(K)<\/span> when K<\/span> is a bicyclic biquadratic number field by means of classical indices, namely, the unit index of K<\/span>, the number of ramified primes, and the number of fundamental units with norm 1 of the quadratic subfields of K<\/span>. Then we study separately the imaginary case and the real case. <\/p>\n\n\n\n

Keywords<\/strong>:<\/span>  P\u00f3lya group, P\u00f3lya field, Biquadratic number field, Ambiguous ideal. <\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 11R20, 11R29; Secondary 13F20.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles What can we say about the P\u00f3lya Group of a Bicyclic Biquadratic Number Field ? Jean-Luc Chabert  LAMFA CNRS-UMR 7352, Universit\u00e9 de Picardie, 80039 Amiens, France. Pages 70-82 | Received 21 October 2022, Accepted 13 January 2023, Published 16 June 2023 Abstract The P\u00f3lya group 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-1719","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1719","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=1719"}],"version-history":[{"count":14,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1719\/revisions"}],"predecessor-version":[{"id":1937,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1719\/revisions\/1937"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=1719"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}