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Application of Greenberg's conjecture in the capitulation problem
Early View
- Author(s): Ali Mouhib
- Article first published online: 11 Oct 2018
- DOI: 10.1002/mana.201700467
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Abstract
Let r be a positive integer. Assume Greenberg's conjecture for some totally real number fields, we show that there exists an infinite family of imaginary cyclic number fields F over the field of rational number field , with an elementary 2‐class group of rank equal to r that capitulates in an unramified quadratic extension over F. Also, we give necessary and sufficient conditions for the Galois group of the unramified maximal 2‐extension over F to be abelian.
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