Geodesic
Isomorphism of Commutative Modular Group Algebras
Serdica Mathematical Journal, Tome 23 (1997) no. 3-4, pp. 211-224.

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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 ∼= KG for some group H, then it is shown that H ∼= G. Let G be a direct sum of cyclic groups, a divisible group or a simply presented torsion abelian group. Then KH ∼= KG as K-algebras for all fields K and some group H if and only if H ∼= G.
Keywords: Isomorphism, Commutative Group Algebras, Units, Direct Sum of Cyclics, Splitting Groups 
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     author = {Danchev, P.},
     title = {Isomorphism of {Commutative} {Modular} {Group} {Algebras}},
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Danchev, P. Isomorphism of Commutative Modular Group Algebras. Serdica Mathematical Journal, Tome 23 (1997) no. 3-4, pp. 211-224. http://geodesic.mathdoc.fr/item/SMJ2_1997_23_3-4_a2/