On Primary Abelian Groups Modulo Finite Subgroups

Abstract

We study the existence of several classes 𝒦 of Abelian p-groups, p a fixed prime, which possess the following property: A ∈ 𝒦⇔A/F ∈ 𝒦, whenever F is a finite subgroup of the Abelian p-group A.

Key Words:

• Almost totally projective groups
• C _λ-groups
• Groups with a nice basis
• Σ-groups
• p ^ω+n -projective groups
• Minimal groups
• Summable groups
• σ-Summable groups
• Totally projective groups

2000 Mathematics Subject Classification:

• 20K10

Notes

Communicated by V. Artamonov.