Geodesic
On metabelian 2-class field towers over $\mathbb Z_2$-extensions of real quadratic fields
Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 795-805

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DOI

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.
DOI : 10.4153/S0008439521000862
Mots-clés : p-class field tower, Z p-extension, Greenberg’s conjecture 
Mizusawa, Yasushi. On metabelian 2-class field towers over $\mathbb Z_2$-extensions of real quadratic fields. Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 795-805. doi: 10.4153/S0008439521000862
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     title = {On metabelian 2-class field towers over $\mathbb Z_2$-extensions of real quadratic fields},
     journal = {Canadian mathematical bulletin},
     pages = {795--805},
     year = {2022},
     volume = {65},
     number = {3},
     doi = {10.4153/S0008439521000862},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000862/}
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