On unramified Galois 2-groups over ℤ₂-extensions of real quadratic fields

Mizusawa, Yasushi

doi:10.1090/S0002-9939-10-10458-4

On unramified Galois $2$-groups over $\mathbb Z_2$-extensions of real quadratic fields
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Proc. Amer. Math. Soc. 138 (2010), 3095-3103 Request permission

Abstract:

We prove that the Galois groups of the maximal unramified pro-$2$-extensions over the cyclotomic $\mathbb Z_2$-extensions of certain real quadratic fields are metacyclic pro-$2$ groups, and we give some criteria for the finiteness and examples relating to Greenberg’s conjecture.

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