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Showing 1 to 7 of 7 for “"Ideal Class Groups"”.
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The Structure of the 2-Sylow Subgroups of the Ideal Class Groups of Imaginary Bicyclic Biquadratic Fields
In this dissertation class groups of imaginary bicyclic biquadratic fields are considered. In chapter 1 we develop a method for determining the structure of the 2-class group of K. In chapters 3, 4, and 5 this method is applied to determine all imaginary bicyclic biquadratic extensions of Q with …
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On the Units and the Structure of the 3-Sylow Subgroups of the Ideal Class Groups of Pure Bicubic Fields and their Normal Closures
… known. Some work has been done on the units, classnumbers and other invariants of the bicubic fields and their normal closures by Parry but no method is available for calculating those invariants. This dissertation provides an algorithm for calculating the number theoretic invariants of the …
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The Structure of the Class Group of Imaginary Quadratic Fields
… Δ. We use the isomorphism between the ideal class groups of the field and the equivalence classes of binary quadratic forms to find the structure of the class group. We determine the structure by combining two of Shanks' algorithms [7, 8]. We utilize this method to find fields with …
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On the Computation of Invariants in non-Normal, non-Pure Cubic Fields and in Their Normal Closures
… prove general results relating the ranks of the ideal class groups of the rings of integers of these cubic fields to those of their normal closures.
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Explicit Composition Identities for Higher Composition Laws in the Quadratic Case
… a very useful way to compute the structure of ideal class groups in quadratic number fields. In addition to that, Gauss composition is also important in the problem of representations of integers by binary quadratic forms. In 2001, Bhargava discovered a new approach to Gauss composition which …
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Iwasawa theory over solvable three-dimensional p-adic Lie extensions
… in the so-called "Iwasawa Main Conjecture". Classically the Main Conjecture (as formulated by Iwasawa himself) involved the behaviour of ideal class groups over cyclotomic Zp-extensions, and related this to the Kubota-Leopoldt p-adic zeta-function. During the last two decades, the main …
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Order computations in generic groups
… over [alpha]... For abelian groups, a random S...G or constant size suffices to compute [lamda](G), the exponent of the group. Having computed [lambda](G), we show that in most cases the structure of an abelian group G can be determined using an additional O(N^[delta]/4) group …