Counting dihedral and quaternionic extensions
نویسندگان
چکیده
منابع مشابه
Counting Dihedral and Quaternionic Extensions
We give asymptotic formulas for the number of biquadratic extensions of Q that admit a quadratic extension which is a Galois extension of Q with a prescribed Galois group, for example, with a Galois group isomorphic to the quaternionic group. Our approach is based on a combination of the theory of quadratic equations with some analytic tools such as the Siegel–Walfisz theorem and the double osc...
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The holomorph of a group G is NormB(λ(G)), the normalizer of the left regular representation λ(G) in its group of permutations B = Perm(G). The multiple holomorph of G is the normalizer of the holomorph in B. The multiple holomorph and its quotient by the holomorph encodes a great deal of information about the holomorph itself and about the group λ(G) and its conjugates within the holomorph. We...
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Let L/F be a dihedral extension of degree 2p, where p is an odd prime. Let K/F and k/F be subextensions of L/F with degrees p and 2, respectively. Then we will study relations between the p-ranks of the class groups Cl(K) and Cl(k). 1. A Short History of Reflection Theorems Results comparing the p-rank of class groups of different number fields (often based on the interplay between Kummer theor...
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This paper is a continuation of [2]. We construct unconditionally several families of number fields with large class numbers. They are number fields whose Galois closures have as the Galois groups, dihedral groups Dn, n = 3, 4, 5, and cyclic groups Cn, n = 4, 5, 6. We first construct families of number fields with small regulators, and by using the strong Artin conjecture and applying some modi...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2011
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-2011-05233-5