Generalized Dieudonné and Honda criteria for primary Abelian groups. (English) Zbl 1154.20043

Danchev, P. V.

Acta Math. Univ. Comen., New Ser. 77, No. 1, 85-91 (2008).

By the classical Kulikov criterion, a \(p\)-group \(G\) is a direct sum of cyclic groups if and only if \(G\) is the union of an ascending chain of subgroups \(G_n\) such that the heights of the nonzero elements in \(G_n\) remain under a finite bound \(k_n\).
In his previous papers the author proved similar results for \(\sigma\)-summable groups, summable groups and \(\Sigma\)-groups. In the present paper he offers an extension of these results to the classes of the so called weakly \(n\)-summable groups and \(n\)-\(\Sigma\)-groups.

Reviewer: Miroslav Ploščica (Košice)

MSC:

20K10	Torsion groups, primary groups and generalized primary groups
20K25	Direct sums, direct products, etc. for abelian groups
20K27	Subgroups of abelian groups

Keywords:

primary Abelian groups; height-finite subgroups; summable groups; Kulikov criterion; direct sums of cyclic groups