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| Paper IPM / M / 17254 |
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| Abstract: | |||||
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For $L/K$ a finite Galois extension of number fields, the relative P\'olya group $Po(L/K)$ coincides with the group of strongly ambiguous ideal classes in $L/K$. In this paper, using a well-known exact sequence related to $Po(L/K)$ in the works of Brumer-Rosen and Zantema, we find short proofs for some classical results in the literature. Then we define the ``Ostrowski quotient'' $Ost(L/K)$ as the cokernel of the capitulation map into $Po(L/K)$ and generalize some known results for $Po(L/\mathbb{Q})$ to $Ost(L/K)$.
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