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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.)

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
20K10 Torsion groups, primary groups and generalized primary groups

Citations:

Zbl 1057.16028
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References:

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