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Isomorphism of commutative group algebras of $p$-mixed splitting groups over rings of characteristic zero
Mathematica Bohemica, Tome 131 (2006) no. 1, pp. 85-93

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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 $p\notin \mathop {\text{inv}}(R) \cup \mathop {\text{zd}}(R)$. 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).
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 $p\notin \mathop {\text{inv}}(R) \cup \mathop {\text{zd}}(R)$. 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).
DOI : 10.21136/MB.2006.134084
Classification : 16S34, 16U60, 20C07, 20K10, 20K21
Keywords: group algebras; isomorphisms; $p$-mixed splitting groups; rings with zero characteristic 
Danchev, Peter. Isomorphism of commutative group algebras of $p$-mixed splitting groups over rings of characteristic zero. Mathematica Bohemica, Tome 131 (2006) no. 1, pp. 85-93. doi: 10.21136/MB.2006.134084
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