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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...”.

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

Citations:

Zbl 0972.16018
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