Advanced Search

If $K/k$ is a finite Galois extension of number fields with Galois group $G$, then the kernel of the capitulation map $C{l}_k\to C{l}_K$ of ideal class groups is isomorphic to the kernel $X\left(H\right)$ of the transfer map $H/H^{\text{'}}\to A,$ where $H=\text{Gal}(\tilde{K}/k),A=\text{Gal}(\tilde{K}/K)$ and $\tilde{K}$ is the Hilbert class field of $K$. H. Suzuki proved that when $G$ is abelian, $\left|G\right|$ divides $\left|X\right(H\left)\right|$. We call a finite abelian group $X$ a transfer kernel for $G$ if $X\cong X\left(H\right)$ for some group extension $A\hookrightarrow H\twoheadrightarrow G$. After characterizing transfer kernels in terms of integral representations of $G$, we show that $X$ is a transfer kernel for...