Sylow \(p\)-subgroups of commutative modular and semisimple group rings. (English) Zbl 0987.16023

The present note is a continuation of the recent paper by the author [C. R. Acad. Bulg. Sci. 54, No. 2, 5-8 (2001; Zbl 0972.16018)]. He announces some results concerning the Sylow subgroups of commutative group rings, including: \(C_\lambda\)-groups; summable groups; direct sums of \(\sigma\)-summable groups; high, basic and divisible subgroups in the modular case; starred groups; basic groups in the semisimple case; Warfield invariants.
Reviewer’s remark: It seems that the self-evaluation given by the author of the note is higher than the results obtained. Such a self-adoration is expressed for example in: “Well, we continue with the announcement of some major facts, obtained by us.”, “We close the work with some new paramount constructions...”, “We conclude the modular case with two central attainments...”.


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
20E07 Subgroup theorems; subgroup growth
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras


Zbl 0972.16018