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Proceedings of the American Mathematical Society

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Modular group algebras of $\aleph_{1}$-separable $p$-groups


Authors: Rüdiger Göbel and Warren May
Journal: Proc. Amer. Math. Soc. 131 (2003), 2987-2992
MSC (2000): Primary 20K10, 20C07; Secondary 20K25, 16S34
Published electronically: January 2, 2003
MathSciNet review: 1993203
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Abstract: Under the assumptions of MA and $\neg$ CH, it is proved that if $F$ is a field of prime characteristic $p$ and $G$ is an $\aleph_{1}$-separable abelian $p$-group of cardinality $\aleph_{1}$, then an isomorphism of the group algebras $FG$ and $FH$ implies an isomorphism of $G$ and $H$.


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Additional Information

Rüdiger Göbel
Affiliation: Fachbereich 6, Mathematik und Informatik, Universität Essen, Universitätsstraße 3, D-45117 Essen, Germany
Email: R.Goebel@uni-essen.de

Warren May
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721
Email: may@math.arizona.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06818-7
Received by editor(s): January 25, 2002
Received by editor(s) in revised form: April 18, 2002
Published electronically: January 2, 2003
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2003 American Mathematical Society