On the full transitivity of a cotorsion hull of a separable primary abelian group

Abstract

We consider the problem of full transitivity of the cotorsion hull $T^{•}$ of a separable primary group T, which is important in describing the lattice of fully invariant subgroups of a group. It is proved that the hull $T^{•}$ is fully transitive if and only if T is the direct sum of the cyclic p-groups or a torsion-complete group.

KEYWORDS:

• Cotorsion hull
• endomorphism ring
• full transitivity of a group
• separable p-group

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20K10
• 20K21
• 20K30

Acknowledgments

I would like to thank the reviewers for careful review they made of the paper and their comments that improved the content of the original text. I also want to describe the respect I have for Dr. Mandi Schaeffer Fry, Associate Editor, for her professional editorial management of the present submission.