Computation of the ideal class group of certain complex quartic fields

Author:
Richard B. Lakein

Journal:
Math. Comp. **28** (1974), 839-846

MSC:
Primary 12A50

DOI:
https://doi.org/10.1090/S0025-5718-1974-0374090-1

MathSciNet review:
0374090

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Abstract: The ideal class group of quartic fields , where , is calculated by a method adapted from the method of cycles of reduced ideals for real quadratic fields. The class number is found in this way for 5000 fields a prime of *F*. A tabulation of the distribution of class numbers shows a striking similarity to that for real quadratic fields with prime discriminant. Also, two fields were found with noncyclic ideal class group .

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DOI:
https://doi.org/10.1090/S0025-5718-1974-0374090-1

Article copyright:
© Copyright 1974
American Mathematical Society