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

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)].


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