Geodesic
A direct factor theorem for commutative group algebras
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 383-387.

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Suppose $F$ is a field of characteristic $p\neq 0$ and $H$ is a $p$-primary abelian $A$-group. It is shown that $H$ is a direct factor of the group of units of the group algebra $F H$.
Classification : 16S34, 16U60, 20C07, 20K10
Keywords: units of group algebras; $A$-groups 
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     title = {A direct factor theorem for commutative group algebras},
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Ullery, William. A direct factor theorem for commutative group algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 383-387. http://geodesic.mathdoc.fr/item/CMUC_1992__33_3_a1/