The Group of Galois Extensions Over Orders in 𝐾𝐶_{𝑝²}

Underwood, Robert

doi:10.1090/S0002-9947-97-01914-4

The Group of Galois Extensions Over Orders in $KC_{p^2}$
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Trans. Amer. Math. Soc. 349 (1997), 1503-1514 Request permission

Abstract:

In this paper we characterize all Galois extensions over $H$ where $H$ is an arbitrary $R$-Hopf order in $KC_{p^{2}}$. We conclude that the abelian group of $H$-Galois extensions is isomorphic to a certain quotient of units groups in $R\times R$. This result generalizes the classification of $H$-Galois extensions, where $H\subset KC_{p}$, due to Roberts, and also to Hurley and Greither.

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