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On metabelian 2-class field towers over 
$\mathbb Z_2$-extensions of real quadratic fields
Published online by Cambridge University Press: 06 October 2021
Abstract
We give a family of real quadratic fields such that the 2-class field towers over their cyclotomic 
$\mathbb Z_2$-extensions have metabelian Galois groups of abelian invariants 
$[2,2,2]$. We also consider the boundedness of the Galois groups in relation to Greenberg’s conjecture, and calculate their class-2 quotients with an explicit example.
MSC classification
Primary:
11R23: Iwasawa theory
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