A direct factor theorem for commutative group algebras. (English) Zbl 0794.16022

The paper extends a result of W. May [Proc. Am. Math. Soc. 76, 31- 34 (1979; Zbl 0388.20041)] to the more general class of \(A\)-groups of R. Warfield [Trans. Am. Math. Soc. 210, 149-168 (1975; Zbl 0324.20058)]. The main theorem states that if \(F\) is a field of positive characteristic \(p\) and if \(H\) is a \(p\)-primary \(A\)-group, then \(H\) is a direct factor of \(U(FH)\).


16U60 Units, groups of units (associative rings and algebras)
20K10 Torsion groups, primary groups and generalized primary groups
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
16S34 Group rings
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