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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 \(U(FH)\).

MSC:

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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