Primary abelian n-Σ-groups

Abstract

We prove the following theorem: Any abelian p-group is an n-Σ-group which is a strong ω-elongation of a totally projective group by a p ω+n -projective group precisely when it is totally projective. In particular, each p-torsion p ω+n -projective n-Σ-group is a direct sum of countable p-groups of length not exceeding ω + n and vice versa. These two claims generalize our recent results in [6] and [7].