On a decomposition formula in commutative group rings. (English) Zbl 1110.16033

Danchev, Peter V.

Miskolc Math. Notes 6, No. 2, 153-159 (2005).

Summary: A necessary and sufficient condition is obtained when the \(p\)-component of the group of all normalized units can be decomposed into two special subgroups provided that the group basis has a standard proper decomposition. The established formula is useful for proving the niceness of certain subgroups in modular group rings and improves our identical claim [in Hokkaido Math. J. 29, No. 2, 255-262 (2000; Zbl 0967.20003)] as well.
We also point out a confusion due to T. Mollov in his reviewer’s report Zbl 0959.20003 concerning our paper [published in Rend. Semin. Mat. Univ. Padova 101, 51-58 (1999)].

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
20K27	Subgroups of abelian groups
20K21	Mixed groups

Keywords:

groups of units; commutative group rings; decompositions; nice subgroups; modular group rings

Citations:

Zbl 0967.20003; Zbl 0959.20003