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.


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