Geodesic
The Tame Kernel of Multi-Cyclic Number Fields
Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 3
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There are many results about the structures of the tame kernels of the number fields. In this paper, we study the structure of those fields $F$, which are the composition of some cyclic number fields, whose degrees over $\mathbb{Q}$ are the same prime number $q$. Then, for any odd prime $p\neq q$, we prove that the $p\mbox{-}$primary part of $K_2\mathcal{O}_F$ is the direct sum of the $p\mbox{-}$primary part of the tame kernels of all the cyclic intermediate fields of $F/\mathbb{Q}$. Moreover, by the approach we developed, we can extend the results to any abelian totally real base field $K$ with trivial $p\mbox{-}$primary tame kernel.
Classification : 11R70 
@article{BMMS_2014_37_3_a16,
     author = {Xia Wu},
     title = {The {Tame} {Kernel} of {Multi-Cyclic} {Number} {Fields}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2014},
     volume = {37},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2014_37_3_a16/}
}
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Xia Wu. The Tame Kernel of Multi-Cyclic Number Fields. Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2014_37_3_a16/