The Journal of the Indian Mathematical Society

Peter V. Danchev ¹

Affiliations
1 Department of Mathematics, Plovdiv University "P. Hilendarski", Plovdiv 4000, BG

Abstract

We define the class K of weakly ω₁-p^ω+n-projectives which consists of abelian p-groups G such that there exists a countable nice subgroup N ⊆ p^ωG with G/(N + p^ω+nG) being p^ω+n-projective. It is shown that K properly contains the class of ω₁-p^ω+n-projectives. More-over, some crucial properties of this new object K are also obtained.

Keywords

Abelian P-Groups, p^ω+n-projective Groups, Countable Sub-Groups, Nice Subgroups, ω₁-p^ω+n-projective Groups, Ulm Subgroups, Ulm Factors.

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Peter V. Danchev ¹

Affiliations
1 Department of Mathematics, Plovdiv University, Plovdiv 4000, BG

Abstract

Suppose κ is an arbitrary ordinal. The concept of κ-bijective homomorphism of abelian groups plays an important role in the modern abelian group theory. We study it in the case of totally projective abelian p-groups, provided κ is uncountable, thus extending some classical results in this way.

Keywords

Abelian Groups, κ-Bijections, Totally Projective Groups.

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