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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The ideal class groups of two cyclotomic fields
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by Frank Gerth PDF
Proc. Amer. Math. Soc. 78 (1980), 321-322 Request permission

Abstract:

It is known that there are exactly two cyclotomic fields with class numbers equal to 8, namely the fields of 29th and 68th roots of unity. We show by elementary methods how to determine the structure of the ideal class groups of these fields.
References
    H. Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper. Ia, Jber. Deutsch. Math.-Verein. 36 (1927), 233-311.
  • John Myron Masley, Solution of small class number problems for cyclotomic fields, Compositio Math. 33 (1976), no. 2, 179–186. MR 450229
  • Edwin Weiss, Algebraic number theory, McGraw-Hill Book Co., Inc., New York-San Francisco-Toronto-London, 1963. MR 0159805
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 78 (1980), 321-322
  • MSC: Primary 12A35; Secondary 12A50
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0553367-5
  • MathSciNet review: 553367