The authors study realizability of metacyclic-nonmodular groups with abelianization Z/2Z x Z/2^m Z as Galois groups of maximal unramified pro-2 extensions over cyclotomic Z2-extensions of fields F=Q(sqrt(eta q r s)), K=Q(sqrt(eta q),sqrt(r s)), and Frohlich fields Q(sqrt(q),sqrt(r),sqrt(s)), plusnew
Benjamin, On the 2-class field tower of some imaginary biquadratic number fields, Ra- manujan J., 11 (2006), 103–110
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On the Existence of the Maximal Unramified Pro-$2$-Extension over the Cyclotomic $\mathbb{Z}_2$-Extension with Prescribed Metacyclic Galois Group
The authors study realizability of metacyclic-nonmodular groups with abelianization Z/2Z x Z/2^m Z as Galois groups of maximal unramified pro-2 extensions over cyclotomic Z2-extensions of fields F=Q(sqrt(eta q r s)), K=Q(sqrt(eta q),sqrt(r s)), and Frohlich fields Q(sqrt(q),sqrt(r),sqrt(s)), plusnew