Geodesic
Groupings of Metabelian Groups and Extension Categories
Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 449-459

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a metabelian group and R an integral domain of characteristic zero, such that no rational prime divisor of │G│ is invertible in R. By RG we denote the group ring of G over R. In this note we shall proveTHEOREM. If RG ≌ RH as R-algebras, then G ≌ HThe question whether this result holds was posed to me by S. K. Sehgal. The result for R = Z is contained in G. Higman's thesis, and he apparently also proved a more general result. At any rate, I think that the methods of the proof are interesting eo ipso, since they establish a “Noether-Deuring theorem” for extension categories.In proving the above result, it is necessary to study closely the category of extensions (gs , S), where the objects are short exact sequences of SG-modules 
Roggenkamp, K. W. Groupings of Metabelian Groups and Extension Categories. Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 449-459. doi: 10.4153/CJM-1980-036-7
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