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Normed unit groups and direct factor problem for commutative modular group algebras. (English) Zbl 0980.16500

Let \(G\) be an Abelian \(p\)-group, \(K\) be a field of characteristic \(p\) and \(V(KG)\) be the group of normalized units in the group algebra \(KG\). Some elementary properties of the group \(V(KG)\) are presented.

MSC:

16U60 Units, groups of units (associative rings and algebras)
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
16S34 Group rings
20K10 Torsion groups, primary groups and generalized primary groups
20K27 Subgroups of abelian groups
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