Quadratic fields with special class groups
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- by James J. Solderitsch PDF
- Math. Comp. 59 (1992), 633-638 Request permission
Abstract:
For every prime number $p \geq 5$ it is shown that, under certain hypotheses on $x \in {\mathbf {Q}}$, the imaginary quadratic fields ${\mathbf {Q}}(\sqrt {{x^{2p}} - 6{x^p} + 1} )$ have ideal class groups with noncyclic p-parts. Several numerical examples with $p = 5$ and 7 are presented. These include the field \[ {\mathbf {Q}}(\sqrt { - 4805446123032518648268510536} ).\] The 7-part of its class group is isomorphic to $C(7) \times C(7) \times C(7)$, where $C(n)$ denotes a cyclic group of order n.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Math. Comp. 59 (1992), 633-638
- MSC: Primary 11R29; Secondary 11R11, 11Y40
- DOI: https://doi.org/10.1090/S0025-5718-1992-1139091-5
- MathSciNet review: 1139091