Abelian groups with a minimal generating set

Abstract

We study the existence of minimal generating sets in abelian groups. We prove that abelian groups with minimal generating sets are closed neither under quotients, nor under subgroups, nor under infinite products.

We give necessary and sufficient conditions for existence of a minimal generating set providing that the abelian group is uncountable, torsion, or torsion-free completely decomposable.

Keywords

• Abelian
• groups
• with
• minimal
• generating
• set