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

Author(s): Robert Underwood
Journal: Trans. Amer. Math. Soc. 349 (1997), 1503-1514.
MSC (1991): Primary 14L15, 16W30, 13B02; Secondary 13B25, 11Sxx
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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
Email: underw@tango.aum.edu

DOI: 10.1090/S0002-9947-97-01914-4
PII: S 0002-9947(97)01914-4
Received by editor(s): June 9, 1995
Copyright of article: Copyright 1997, American Mathematical Society

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