Danchev, P. V. Isomorphism of commutative modular group algebras. (English) Zbl 0977.20003 Serdica Math. J. 23, No. 3-4, 211-224 (1997). Summary: 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 \(KH\cong KG\) for some group \(H\), then it is shown that \(H\cong G\).Let \(G\) be a direct sum of cyclic groups, a divisible group or a simply presented torsion Abelian group. Then \(KH\cong KG\) as \(K\)-algebras for all fields \(K\) and some group \(H\) if and only if \(H\cong G\). Cited in 1 Document MSC: 20C07 Group rings of infinite groups and their modules (group-theoretic aspects) 16S34 Group rings Keywords:commutative group algebras; isomorphism problem; direct sums of cyclic groups; simply presented torsion Abelian groups PDFBibTeX XMLCite \textit{P. V. Danchev}, Serdica Math. J. 23, No. 3--4, 211--224 (1997; Zbl 0977.20003) Full Text: EuDML