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commutative group algebras; isomorphism
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.
[K] Karpilovsky G.: Commutative Group Algebras. Marcel Dekker New York (1983). MR 0704185 | Zbl 0508.16010
[M] May W.: Isomorphism of group algebras. J. Algebra 40 (1976), 10-18. MR 0414618 | Zbl 0329.20002
[U] Ullery W.: On isomorphism of group algebras of torsion abelian groups. Rocky Mtn. J. Math. 22 (1992), 1111-1122. MR 1183707 | Zbl 0773.16008
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