Geodesic
A note on group algebras of $p$-primary abelian groups
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 1, pp. 11-14.

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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.
Classification : 16S34, 20C07, 20K10
Keywords: commutative group algebras; isomorphism 
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     title = {A note on group algebras of $p$-primary abelian groups},
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Ullery, William. A note on group algebras of $p$-primary abelian groups. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 1, pp. 11-14. http://geodesic.mathdoc.fr/item/CMUC_1995__36_1_a2/