1 results
On metabelian 2-class field towers over
$\mathbb Z_2$
-extensions of real quadratic fields
- Part of
-
- Journal:
- Canadian Mathematical Bulletin / Volume 65 / Issue 3 / September 2022
- Published online by Cambridge University Press:
- 06 October 2021, pp. 795-805
- Print publication:
- September 2022
-
- Article
- Export citation
-
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.
