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\(G\)-unipotent units in commutative group rings. (English) Zbl 1207.16039

Summary: We find a necessary and sufficient condition under which all normalized units in a commutative group ring with prime characteristic \(p>0\) are \(G\)-unipotent units. This continues our recent investigation on idempotent units in commutative group rings [published in Kochi J. Math. 4, 61-68 (2009; Zbl 1182.16031)] and also strengthens our own results [from Extr. Math. 23, No. 1, 49-60 (2008; Zbl 1163.16019)].

MSC:

16U60 Units, groups of units (associative rings and algebras)
16S34 Group rings
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
20K21 Mixed groups
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