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Transactions of the American Mathematical Society

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The Group of Galois Extensions
Over Orders in $KC_{p^{2}}$

Author: Robert Underwood
Journal: Trans. Amer. Math. Soc. 349 (1997), 1503-1514
MSC (1991): Primary 14L15, 16W30, 13B02; Secondary 13B25, 11Sxx
MathSciNet review: 1407713
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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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Additional Information

Robert Underwood
Affiliation: Department of Mathematics, Auburn University at Montgomery, Montgomery, Alabama 36117

Received by editor(s): June 9, 1995
Article copyright: © Copyright 1997 American Mathematical Society