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The structure of the unramified abelian Iwasawa module of some number fields

Ali Mouhib

Vol. 323 (2023), No. 1, 173–184
DOI: 10.2140/pjm.2023.323.173
Abstract

For a given positive integer m, we determine an explicit infinite family of real quadratic number fields F, such that the unramified abelian Iwasawa module over the 2-extension of F, is isomorphic to (2)2m .

Keywords
class group, unit group, capitulation problem, $Z_2$-extension
Mathematical Subject Classification
Primary: 11R23, 11R29, 11R32, 11R37
Milestones
Received: 25 October 2022
Revised: 28 February 2023
Accepted: 1 April 2023
Published: 29 May 2023
Authors
Ali Mouhib
Department of Mathematics
Sciences and Engineering Laboratory
Polydisciplinary Faculty of Taza
Sidi Mohamed Ben Abdellah University
Taza-Gare
Morocco

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