2 results
On metabelian 2-class field towers over
$\mathbb Z_2$
-extensions of real quadratic fields
- Part of
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- 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
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- Article
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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.
Iwasawa Theory for K2n
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- Journal:
- Journal of K-Theory / Volume 12 / Issue 1 / August 2013
- Published online by Cambridge University Press:
- 02 May 2013, pp. 115-123
- Print publication:
- August 2013
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- Article
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Given a number field F and a prime number p; let Fn denote the cyclotomic extension with [Fn : F] = pn; and let
denote its ring of integers. We establish an analogue of the classical Iwasawa theorem for the orders of K2i (){p}.
denote its ring of integers. We establish an analogue of the classical Iwasawa theorem for the orders of 