Geodesic
Group algebras of generalized primary groups
Matematičeskie zametki, Tome 16 (1974) no. 3, pp. 399-405.

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A number of the known results concerning group algebras of primary groups carry over to group algebras of generalized primary groups. In particular, we show that the group algebra $LG$ of a generalized primary (relative to the prime $p$) group $G$ over the ring $L$, in which the element $p$ is not invertible, determines, to within an isomorphism, a basis subgroup of the generalized primary group $G$. In addition, we indicate two classes of composite abelian groups which are determined, to within an isomorphism, by their group algebras over the ring $L$. 
@article{MZM_1974_16_3_a6,
     author = {Yu. M. Firsov},
     title = {Group algebras of generalized primary groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {399--405},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a6/}
}
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Yu. M. Firsov. Group algebras of generalized primary groups. Matematičeskie zametki, Tome 16 (1974) no. 3, pp. 399-405. http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a6/