What question did this study set out to answer?

The study aims to investigate TI-groups within the class of mixed abelian quotient divisible groups with torsion-free rank 1.

March 15, 2026

TI-Groups in the Class of Quotient Divisible Abelian Groups

Key Points

The study aims to investigate TI-groups within the class of mixed abelian quotient divisible groups with torsion-free rank 1.
Defined and analyzed the class of mixed abelian quotient divisible groups.
Examined the invariants such as torsion part and height-matrices.
Described TI-groups through the lens of their cocharacteristics.
Established a relationship between TI-groups and their invariants in the quotient divisible group class.
Described the characteristics that define TI-groups uniquely in this context.
Showed that every group in the class can be represented through its cocharacteristic.

Abstract

We consider the class QD1 of mixed abelian quotient divisible groups of torsion-free rank 1. Groups from this class, as well as countable mixed abelian groups of rank 1 are determined by their own torsion part and the class of equivalent height-matrices, which are invariants of such groups. On the other hand, every group from QD1 can be described by its cocharacteristic. An abelian group G is called a TI -group if every associative ring on G is filial. In the class QD1 TI -groups are described in the language of these invariants.

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