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On unramified Galois $ 2$-groups over $ \mathbb{Z}_2$-extensions of real quadratic fields


Author: Yasushi Mizusawa
Journal: Proc. Amer. Math. Soc. 138 (2010), 3095-3103
MSC (2010): Primary 11R23; Secondary 11R20
DOI: https://doi.org/10.1090/S0002-9939-10-10458-4
Published electronically: May 4, 2010
MathSciNet review: 2653934
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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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Additional Information

Yasushi Mizusawa
Affiliation: Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa, Nagoya, Aichi, 466-8555 Japan
Email: mizusawa.yasushi@nitech.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-10-10458-4
Received by editor(s): June 19, 2009
Received by editor(s) in revised form: November 29, 2009
Published electronically: May 4, 2010
Additional Notes: This work was supported by KAKENHI (20840022), Grant-in-Aid for Young Scientists (Start-up).
Communicated by: Ken Ono
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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