{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:10:44Z","timestamp":1776795044856,"version":"3.51.2"},"reference-count":24,"publisher":"American Mathematical Society (AMS)","issue":"277","license":[{"start":{"date-parts":[[2012,7,1]],"date-time":"2012-07-01T00:00:00Z","timestamp":1341100800000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper, assuming the Generalized Riemann Hypothesis, we determine all imaginary abelian number fields\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N\">\n                        <mml:semantics>\n                          <mml:mi>N<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">N<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of 2-power degrees with ideal class groups of exponents\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"less-than-or-equal-to 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\le 2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for which the 2-ranks of the Galois group of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N\">\n                        <mml:semantics>\n                          <mml:mi>N<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">N<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    over\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper Q\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:mi mathvariant=\"double-struck\">Q<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {Q}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    are equal to 2.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2011-02509-3","type":"journal-article","created":{"date-parts":[[2011,7,1]],"date-time":"2011-07-01T08:34:50Z","timestamp":1309509290000},"page":"533-554","source":"Crossref","is-referenced-by-count":0,"title":["The imaginary abelian number fields of 2-power degrees with ideal class groups of exponent \u22642"],"prefix":"10.1090","volume":"81","author":[{"given":"Jeoung-Hwan","family":"Ahn","sequence":"first","affiliation":[]},{"given":"Soun-Hi","family":"Kwon","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2011,7,1]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/s00605-002-0499-7","article-title":"Lower bounds for the height and size of the ideal class group in CM-fields","volume":"138","author":"Amoroso, Francesco","year":"2003","journal-title":"Monatsh. 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