Abstract
AbstractWe 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.
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