Trim Extensions of Mixed Groups

Abstract

If G is an extension of an Abelian group H with G/H torsion, call H ⊆ G a trim extension if, for each relevant prime p of G/H, the p-primary component of the torsion subgroup of G is torsion complete. In this article we give necessary and sufficient conditions for two trim extensions of a group H to be equivalent. We also characterize equivalent extension types (as defined by Baer). The class of trim extensions is more general than the class of slim extensions recently introduced by Hill and Megibben.

Key Words:

• Baer's equivalent
• Equivalent extensions
• Extension types
• Trim extension

2000 Mathematics Subject Classification:

• 20K35

Notes

Communicated by A. Facchini.