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Mathematische Nachrichten > 292 > 3 > 633 - 639
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...
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Mathematische Nachrichten > 289 > 14-15 > 1927 - 1933
We study the capitulation problem of the 2‐class group of some cyclic number fields M with large degree and 2‐class group isomorphic to . Precisely, we give the structure of the Galois group of the maximal unramified 2‐extension over M.
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Mathematische Zeitschrift > 2000 > 233 > 2 > 251-263
Abstract. We explicitly calculate all the 2-primary higher algebraic K-groups of the rings of integers of all 2-regular quadratic number fields, cyclotomic number fields, or maximal real subfields of such. Here 2-regular means that (2) does not split in the number field, and its narrow Picard group is of odd order.
