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Title: A note on group algebras of $p$-primary abelian groups (English)
Author: Ullery, William
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 36
Issue: 1
Year: 1995
Pages: 11-14
Category: math
Summary: Suppose $p$ is a prime number and $R$ is a commutative ring with unity of characteristic 0 in which $p$ is not a unit. Assume that $G$ and $H$ are $p$-primary abelian groups such that the respective group algebras $RG$ and $RH$ are $R$-isomorphic. Under certain restrictions on the ideal structure of $R$, it is shown that $G$ and $H$ are isomorphic. (English)
Keyword: commutative group algebras
Keyword: isomorphism
MSC: 16S34
MSC: 20C07
MSC: 20K10
idZBL: Zbl 0828.20005
idMR: MR1334408
Date available: 2009-01-08T18:15:35Z
Last updated: 2012-04-30
Stable URL:
Reference: [K] Karpilovsky G.: Commutative Group Algebras.Marcel Dekker New York (1983). Zbl 0508.16010, MR 0704185
Reference: [M] May W.: Isomorphism of group algebras.J. Algebra 40 (1976), 10-18. Zbl 0329.20002, MR 0414618
Reference: [U] Ullery W.: On isomorphism of group algebras of torsion abelian groups.Rocky Mtn. J. Math. 22 (1992), 1111-1122. Zbl 0773.16008, MR 1183707


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