×

Sylow \(p\)-subgroups of modular Abelian group rings. (English) Zbl 0972.16018

The author studies the group \(V(RG)\) of units with augmentation 1 of the group algebra \(RG\) of an Abelian group \(G\) over a commutative unitary ring \(R\) of prime characteristic \(p\). The main results give relations between \(V(RG)\) and \(V(RH)\) for subgroups \(H\) of \(G\) and, under some minimal restrictions on \(R\) and \(G\), criteria for the factors \(V(RG)/V(RH)\) to belong to some major classes of Abelian groups.

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)
20K10 Torsion groups, primary groups and generalized primary groups
PDFBibTeX XMLCite