Is There a Core Class for Almost Free Groups of Size ℵ₁?

Abstract

We discuss the prospects for finding a “core class,” i.e., a well-behaved class of non-free abelian groups of cardinality ℵ₁ such that every non-free abelian group of cardinality ℵ₁ has a subgroup in the core class.

Key Words:

• Abelian groups
• Almost free
• Core class

Acknowledgments

We thank the referee for his helpful comments and in particular for bringing to our attention the references Eklof et al.(1984), and Mekler (1983 1987). Blass was partially supported by NSF grant DMS 0070723.

Notes

^#Communicated by K. Rangaswamy.