On unramified Galois $2$-groups over $\mathbb Z_2$-extensions of real quadratic fields
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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 Greenbergβs conjecture.References
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Additional Information
- Yasushi Mizusawa
- Affiliation: Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa, Nagoya, Aichi, 466-8555 Japan
- MR Author ID: 672607
- Email: mizusawa.yasushi@nitech.ac.jp
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2653934