Subgroups of the basic subgroup in a modular group ring. (English) Zbl 1112.16030

This paper is a continuation of the author’s previous papers on group rings, especially of [P. Danchev, Math. Bohem. 129, No. 1, 79-90 (2004; Zbl 1057.16028)].
Let \(R\) be a unitary commutative ring of prime characteristic \(p\) and let \(G\) be an Abelian group with \(p\)-component denoted by \(G_p\). Let \(S(RG)\) be the normed Sylow \(p\)-group in the group ring \(RG\). The main result of the present paper is that \(S(RG)\) and \(S(RG)/G_p\) are both starred, provided \(G_p\) is not divisible. (An Abelian \(p\)-group is called starred if it has the same power as its basic subgroup.)


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
20K10 Torsion groups, primary groups and generalized primary groups


Zbl 1057.16028
Full Text: EuDML


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