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MATHEMATICA BOHEMICA, Vol. 131, No. 1, pp. 85-93 (2006)
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#
Isomorphism of commutative group algebras

of $p$-mixed splitting groups over rings

of characteristic zero

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Peter Danchev

* Peter Danchev*, 13, General Kutuzov Street, block 7, floor 2, apartment 4, 4003 Plovdiv, Bulgaria-BGR, e-mail: ` pvdanchev@yahoo.com`

**Abstract:** 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).

**Keywords:** group algebras, isomorphisms, $p$-mixed splitting groups, rings with zero characteristic

**Classification (MSC2000):** 20C07, 16S34, 16U60, 20K10, 20K21

**Full text of the article:**

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