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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… Click to show full 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 Q, 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.
Keywords:
capitulation problem;
application greenberg;
conjecture;
greenberg conjecture;
number;
conjecture capitulation
Journal Title: Mathematische Nachrichten
Year Published: 2018
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Journal Title: Mathematische Nachrichten
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!