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Keywords:
class field tower; class group; real quadratic number field; metacyclic group
class field tower; class group; real quadratic number field; metacyclic group
Summary:
We begin by giving a criterion for a number field $K$ with 2-class group of rank 2 to have a metacyclic Hilbert 2-class field tower, and then we will determine all real quadratic number fields $\mathbb Q(\sqrt d)$ that have a metacyclic nonabelian Hilbert $2$-class field tower.
References:
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