Computation of the ideal class group of certain complex quartic fields
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- by Richard B. Lakein PDF
- Math. Comp. 28 (1974), 839-846 Request permission
Abstract:
The ideal class group of quartic fields $K = F(\sqrt \mu )$, where $F = {\mathbf {Q}}(i)$, 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 $K = F(\sqrt \pi ),\pi \equiv \pm 1 \bmod 4,\pi$ 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 $C(3) \times C(3)$.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 839-846
- MSC: Primary 12A50
- DOI: https://doi.org/10.1090/S0025-5718-1974-0374090-1
- MathSciNet review: 0374090