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Suppose $G$ is a $p$ -mixed splitting abelian group and $R$ is a commutative unitary ring of zero characteristic such that the prime number $p$ satisfies $p \notin inv (R) \cup zd (R)$ . Then $R (H)$ and $R (G)$ are canonically isomorphic $R$ -group algebras for any group $H$ precisely when $H$ and $G$ are isomorphic groups. This statement strengthens results due to W. May published in J. Algebra (1976) and to W. Ullery published in Commun. Algebra (1986), Rocky Mt. J. Math. (1992) and Comment. Math. Univ. Carol. (1995).

Isomorphism of Commutative Modular Group Algebras

Danchev, P. (1997)

Serdica Mathematical Journal

∗ The work was supported by the National Fund “Scientific researches” and by the Ministry of Education and Science in Bulgaria under contract MM 70/91.Let K be a field of characteristic p > 0 and let G be a direct sum of cyclic groups, such that its torsion part is a p-group. If there exists a K-isomorphism KH ∼= KG for some group H, then it is shown that H ∼= G. Let G be a direct sum of cyclic groups, a divisible group or a simply presented torsion abelian group. Then KH ∼= KG as K-algebras...

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Idempotents in complex group rings: Theorems of Zalesskij and Bass revisited.

Idempotents in Group Rings.

Indecomposable Modules with Cyclic Vertex.

Induced Modules and Affine Quotients.

Isométries de caractères et équivalences de Morita ou dérivées

Isomorphe Gruppenringe lokal endlicher Gruppen.

Isomorphism of commutative group algebras of $p$ -mixed splitting groups over rings of characteristic zero

Isomorphism of Commutative Modular Group Algebras

Isomorphism of modular group algebras of direct sums of torsion-complete abelian $p$ -groups

Isomorphism of noncommutative group algebras of torsion-free groups over a field.

Isomorphisms and automorphisms of integral group rings

Isomorphisms of p-adic Group Rings.

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