منابع مشابه
Infinite Hilbert Class Field Towers over Cyclotomic Fields
Weuse a result of Y. Furuta to show that for almost all positive integers m, the cyclotomic field (exp(2π i/m)) has an infinite Hilbert p-class field tower with high rankGalois groups at each step, simultaneously for all primes p of size up to about (log logm)1+o(1). We also use a recent result of B. Schmidt to show that for infinitely many m there is an infinite Hilbert p-class field tower ove...
متن کاملCounting Manifolds and Class Field Towers
In [BGLM] and [GLNP] it was conjectured that if H is a simple Lie group of real rank at least 2, then the number of conjugacy classes of (arithmetic) lattices in H of covolume at most x is x log x/ log log x where γ(H) is an explicit constant computable from the (absolute) root system of H . In this paper we prove that this conjecture is false. In fact, we show that the growth is at rate x log ...
متن کاملInfinite Towers of Tree Lattices
is finite, and a uniform X-lattice if Γ\X is a finite graph, non-uniform otherwise ([BL], Ch. 3). Bass and Kulkarni have shown ([BK], (4.10)) that G = Aut(X) contains a uniform X-lattice if and only if X is the universal covering of a finite connected graph, or equivalently, that G is unimodular, and G\X is finite. In this case, we call X a uniform tree. Following ([BL], (3.5)) we call X rigid ...
متن کاملOn 2-class field towers of imaginary quadratic number fields
For a number field k, let k1 denote its Hilbert 2-class field, and put k2 = (k1)1. We will determine all imaginary quadratic number fields k such that G = Gal(k2/k) is abelian or metacyclic, and we will give G in terms of generators and relations.
متن کاملOn 2-class Field Towers of Some Imaginary Quadratic Number Fields
We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2, 2, 2) whose Hilbert 2-class fields are finite.
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2009
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-009-0334-8