<?xml version="1.0" encoding="utf-8"?>
<journal>
  <journal_metadata lang="en">
    <full_title>Bulletin of the Australian Mathematical
    Society</full_title>
    <abbrev_title>Bull. Austral. Math. Soc.</abbrev_title>
    <issn media_type="online">0004-9727</issn>
    <coden>ALNBAB</coden>
  </journal_metadata>
  <journal_issue>
    <publication_date media_type="online">
      <year>2005</year>
    </publication_date>
    <journal_volume>
      <volume>72</volume>
    </journal_volume>
    <issue>3</issue>
    <doi_data>
      <doi>10.wxyz/CV72P3</doi>
      <resource>
      http://www.austms.org.au/Publ/Bulletin/V72P3/</resource>
    </doi_data>
  </journal_issue>
  <journal_article publication_type="full_text">
    <titles>
      <title>On 3-class groups of certain pure cubic fields</title>
    </titles>
    <contributors>
      <person_name sequence="first" contributor_role="author">Frank
      Gerth III</person_name>
    </contributors>
    <publication_date media_type="online">
      <given_date>13 February 2006</given_date>
      <year>2006</year>
      <month>2</month>
      <day>13</day>
    </publication_date>
    <pages>
      <first_page>471</first_page>
      <last_page>476</last_page>
    </pages>
    <publisher_item>
      <item_number>723-5238-GeIII-2005</item_number>
    </publisher_item>
    <doi_data>
      <doi>10.wxyz/C2005V72P3p471</doi>
      <resource>
      http://www.austms.org.au/Publ/Bulletin/V72P3/723-5238-GeIII/</resource>
    </doi_data>
    <extra_info>
      <abstract>Recently Calegari and Emerton made a conjecture
      about the 3-class groups of certain pure cubic fields and
      their normal closures. This paper proves their conjecture and
      provides additional insight into the structure of the 3-class
      groups of pure cubic fields and their normal
      closures.</abstract>
      <subject_class>11R16, 11R29</subject_class>
      <acknowledgement></acknowledgement>
    </extra_info>
    <citation_list>
      <citation>
        <structured_citation>
          <author>P. Barrucand and H. Cohn</author>
          <title type="article">Remarks on principal factors in a
          relative cubic field</title>
          <medium type="journal" volume="3" year="1971"
          pages="226--239">J. Number Theory</medium>
          <MRnumber>MR276197</MRnumber>
        </structured_citation>
        <unstructured_citation style="LaTeX">P. Barrucand and H.
        Cohn; Remarks on principal factors in a relative cubic
        field, \textit{J. Number Theory} \textbf{3} (1971),
        pp.~226--239.</unstructured_citation>
      </citation>
      <citation>
        <structured_citation>
          <author>P. Barrucand, H. Williams and L. Baniuk</author>
          <title type="article">A computational technique for
          determining the class number of a pure cubic
          field</title>
          <medium type="journal" volume="30" year="1976"
          pages="312--323">Math. Comp.</medium>
          <MRnumber>MR392913</MRnumber>
        </structured_citation>
        <unstructured_citation style="LaTeX">P. Barrucand, H.
        Williams and L. Baniuk; A computational technique for
        determining the class number of a pure cubic field,
        \textit{Math. Comp.} \textbf{30} (1976),
        pp.~312--323.</unstructured_citation>
      </citation>
      <citation>
        <structured_citation>
          <author>F. Calegari and M. Emerton</author>
          <title type="article">On the ramification of Hecke
          algebras at Eisenstein primes</title>
          <medium type="journal" volume="160" year="2005"
          pages="97--144">Invent. Math.</medium>
          <MRnumber>MR2129709</MRnumber>
        </structured_citation>
        <unstructured_citation style="LaTeX">F. Calegari and M.
        Emerton; On the ramification of Hecke algebras at
        Eisenstein primes, \textit{Invent. Math.} \textbf{160}
        (2005), pp.~97--144.</unstructured_citation>
      </citation>
      <citation>
        <structured_citation>
          <author>F. Gerth</author>
          <title type="article">On 3-class groups of pure cubic
          fields</title>
          <medium type="journal" volume="278/279" year="1975"
          pages="52--62">J. Reine Angew. Math.</medium>
          <MRnumber>MR387234</MRnumber>
        </structured_citation>
        <unstructured_citation style="LaTeX">F. Gerth; On 3-class
        groups of pure cubic fields, \textit{J. Reine Angew. Math.}
        \textbf{278/279} (1975),
        pp.~52--62.</unstructured_citation>
      </citation>
      <citation>
        <structured_citation>
          <author>F. Gerth</author>
          <title type="article">Ranks of 3-class groups of
          non-Galois cubic fields</title>
          <medium type="journal" volume="30" year="1976"
          pages="307--322">Acta Arith.</medium>
          <MRnumber>MR422198</MRnumber>
        </structured_citation>
        <unstructured_citation style="LaTeX">F. Gerth; Ranks of
        3-class groups of non-Galois cubic fields, \textit{Acta
        Arith.} \textbf{30} (1976),
        pp.~307--322.</unstructured_citation>
      </citation>
      <citation>
        <structured_citation>
          <author>G. Gras</author>
          <title type="article">Sur les 
          <span class="MATH">
            <i>ℓ</i>
          </span>-classes d'idéaux des extensions non galoisiennes
          de 
          <span class="MATH">
            <i>\mathbb Q</i>
          </span>de degré premier impair 
          <span class="MATH">
            <i>ℓ</i>
          </span>a clôture galoisienne diédrale de degré 
          <span class="MATH">
            <i>2ℓ</i>
          </span></title>
          <medium type="journal" volume="26" year="1974"
          pages="677--685">J. Math. Soc. Japan</medium>
          <MRnumber>MR364179</MRnumber>
        </structured_citation>
        <unstructured_citation style="LaTeX">G. Gras; Sur les $\ell
        $-classes d'id\'eaux des extensions non galoisiennes de
        ${\mathbb Q}$ de degr\'e premier impair $\ell $ a cl\^oture
        galoisienne di\'edrale de degr\'e $2\ell $, \textit{J.
        Math. Soc. Japan} \textbf{26} (1974),
        pp.~677--685.</unstructured_citation>
      </citation>
      <citation>
        <structured_citation>
          <author>T. Honda</author>
          <title type="article">Pure cubic fields whose class
          numbers are multiples of three</title>
          <medium type="journal" volume="3" year="1971"
          pages="7--12">J. Number Theory</medium>
          <MRnumber>MR292795</MRnumber>
        </structured_citation>
        <unstructured_citation style="LaTeX">T. Honda; Pure cubic
        fields whose class numbers are multiples of three,
        \textit{J. Number Theory} \textbf{3} (1971),
        pp.~7--12.</unstructured_citation>
      </citation>
      <citation>
        <structured_citation>
          <author>L. Washington</author>
          <title type="book" year="1982">Introduction to cyclotonic
          fields</title>
          <publisher address="New York">Springer-Verlag</publisher>
          <MRnumber>MR718674</MRnumber>
        </structured_citation>
        <unstructured_citation style="LaTeX">L. Washington;
        \textit{Introduction to cyclotonic fields}
        (Springer-Verlag, New York, 1982).</unstructured_citation>
      </citation>
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  </journal_article>
</journal>
