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Relative integral bases for quartic fields over quadratic subfields

โœ Scribed by B. K. Spearman; K. S. Williams


Publisher
Akadmiai Kiad
Year
1996
Tongue
English
Weight
306 KB
Volume
70
Category
Article
ISSN
1588-2632

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Suppose that L#K are abelian extensions of the rationals Q with Galois groups (Zร‚q s Z) n and (Zร‚q r Z) m , respectively, q any prime number. It is proved that Lร‚K has a relative integral basis under certain simple conditions. In particular, [L : K] q s or q s +1 (according to q is odd or even) is e

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Focusing on a particular case, we will show that one can explicitly determine the quartic fields \(\mathbf{K}\) that have ideal class groups of exponent \(\leqslant 2\), provided that \(\mathbf{K} / \mathbf{Q}\) is not normal, provided that \(\mathbf{K}\) is a quadratic extension of a fixed imaginar