{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T04:56:56Z","timestamp":1785214616415,"version":"3.55.0"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T00:00:00Z","timestamp":1605830400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T00:00:00Z","timestamp":1605830400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s10998-020-00362-x","type":"journal-article","created":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T13:03:14Z","timestamp":1605877394000},"page":"54-66","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["On the maximal unramified pro-2-extension of certain cyclotomic $$\\mathbb {Z}_2$$-extensions"],"prefix":"10.1007","volume":"83","author":[{"given":"Abdelmalek","family":"Azizi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammed","family":"Rezzougui","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdelkader","family":"Zekhnini","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,11,20]]},"reference":[{"key":"362_CR1","doi-asserted-by":"publisher","first-page":"2741","DOI":"10.1090\/S0002-9947-01-02753-2","volume":"7","author":"A Azizi et","year":"2001","unstructured":"A. Azizi et, A. Mouhib, Sur le rang du 2-groupe de classes de $$(\\mathbb{Q} \\sqrt{m},\\sqrt{d} )$$ o\u00fa m = 2 ou un premier p = 1 mod 4. Trans. Am. Math. Soc. 7, 2741\u20132752 (2001)","journal-title":"Trans. Am. Math. Soc."},{"issue":"1","key":"362_CR2","doi-asserted-by":"publisher","first-page":"17","DOI":"10.2140\/pjm.2005.218.17","volume":"218","author":"A Azizi","year":"2005","unstructured":"A. Azizi, A. Mouhib, Capitulation des 2- classes d\u2019id\u00e9aux de certains corps biquadratiques dont le corps de genres diff\u00e8re du 2-corps de classes de Hilbert. Pac. J. Math. 218(1), 17\u201336 (2005)","journal-title":"Pac. J. Math."},{"issue":"04","key":"362_CR3","doi-asserted-by":"publisher","first-page":"807","DOI":"10.1142\/S179304211950043X","volume":"15","author":"A Azizi","year":"2019","unstructured":"A. Azizi, M. Rezzougui, M. Taous, A. Zekhnini, On the Hilbert 2-class field of some quadratic number fields. Int. J. Number Theory. 15(04), 807\u2013824 (2019)","journal-title":"Int. J. Number Theory."},{"issue":"4","key":"362_CR4","first-page":"1163","volume":"69","author":"E Benjamin","year":"2018","unstructured":"E. Benjamin, C. Snyder, On the rank of 2- class group of the Hilbert 2-class field of some quadratic fields. Quart. J. Math 69(4), 1163\u20131193 (2018)","journal-title":"Quart. J. Math"},{"key":"362_CR5","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1017\/S0305004100033521","volume":"54","author":"N Blackburn","year":"1958","unstructured":"N. Blackburn, On prime-power groups with two generators. Proc. Camb. Philos. Math. Soc. 54, 327\u2013337 (1958)","journal-title":"Proc. Camb. Philos. Math. Soc."},{"key":"362_CR6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511470882","volume-title":"Analytic Pro-p Groups","author":"JD Dixon","year":"1999","unstructured":"J.D. Dixon, M.P.F. du Sautoy, A. Mann, D. Segal, Analytic Pro-p Groups, 2nd edn. (Cambridge Studies in Advanced Mathematics, Cambridge, 1999)","edition":"2"},{"key":"362_CR7","first-page":"264","volume":"70","author":"T Fukuda","year":"1994","unstructured":"T. Fukuda, Remarks on $$\\mathbb{Z}_p$$- extension of number fields. Proc. Japan Acad. Ser. A 70, 264\u2013266 (1994)","journal-title":"Proc. Japan Acad. Ser. A"},{"key":"362_CR8","doi-asserted-by":"publisher","first-page":"fasc. 3","DOI":"10.5802\/aif.480","volume":"23","author":"G Gras","year":"1973","unstructured":"G. Gras, Sur les l-classes d\u2019id\u00e9aux dans les extensions cycliques relatives de degr\u00e9 premier l. Ann. Inst. Fourier Grenoble 23, fasc. 3 (1973)","journal-title":"Ann. Inst. Fourier Grenoble"},{"key":"362_CR9","doi-asserted-by":"publisher","first-page":"263","DOI":"10.2307\/2373625","volume":"98","author":"R Greenberg","year":"1976","unstructured":"R. Greenberg, On the Iwasawa invariants of totally real number fields. Am. J. Math. 98, 263\u2013284 (1976)","journal-title":"Am. J. Math."},{"key":"362_CR10","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1515\/crll.1930.162.134","volume":"162","author":"H Hasse","year":"1930","unstructured":"H. Hasse, Neue Begr\u00fcndung der Theorie des Normenrestsymbols. J. Reine Angew. Math. 162, 134\u2013143 (1930)","journal-title":"J. Reine Angew. Math."},{"key":"362_CR11","volume-title":"The Theory of Groups","author":"M Hall","year":"1959","unstructured":"M. Hall, The Theory of Groups (Macmillan, New York, 1959)"},{"key":"362_CR12","volume-title":"Algebric Number Fields","author":"GJ Janusz","year":"1973","unstructured":"G.J. Janusz, Algebric Number Fields (Academic press, New-York, 1973)"},{"key":"362_CR13","unstructured":"F. Lemmermeyer, The development of the principal genus theorem,arXiv:Math\/0207306v1"},{"key":"362_CR14","first-page":"289","volume":"7","author":"K Miyake","year":"1989","unstructured":"K. Miyake, Algebraic investigations of Hilbert\u2019s Theorem 94, the principal ideal theorem and capitulation problem. Expos. Math. 7, 289\u2013346 (1989)","journal-title":"Expos. Math."},{"issue":"1","key":"362_CR15","doi-asserted-by":"publisher","first-page":"93","DOI":"10.4064\/aa119-1-7","volume":"119","author":"Y Mizusawa","year":"2005","unstructured":"Y. Mizusawa, On the maximal unramified pro-2- extension of $$\\mathbb{Z}_2$$- extensions of certain real quadratic fields II. Acta Arith. 119(1), 93\u2013107 (2005)","journal-title":"Acta Arith."},{"key":"362_CR16","first-page":"69","volume":"170","author":"L R\u00e9dei","year":"1933","unstructured":"L. R\u00e9dei, H. Reichardt, Die Anzahl der durch 4 teilbaren Invarianten der Klassengruppe eines beliebigen quadratischen Zahlk\u00f6rpers. J. Reine Angew. Math. 170, 69\u201374 (1933)","journal-title":"J. Reine Angew. Math."}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-020-00362-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10998-020-00362-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-020-00362-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,29]],"date-time":"2022-11-29T02:08:50Z","timestamp":1669687730000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10998-020-00362-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,20]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["362"],"URL":"https:\/\/doi.org\/10.1007\/s10998-020-00362-x","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"value":"0031-5303","type":"print"},{"value":"1588-2829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,20]]},"assertion":[{"value":"4 May 2020","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 November 2020","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}