** Canan Özeren, **Dokuz Eylül University.

**Date**: 26th of December, 2022, Tuesday,

**Time**: 13:30 – 15:30.

**Place**: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206

**.****Abstract**:Torsion-free covers exist for abelian groups (see [1]).

The coGalois group of a torsion-free cover of an abelian group is defined in [2] as the group of s.t. and is denoted by .

The abelian groups for which the coGalois group is trivial characterized in [3].

The notion of coGalois group can be defined in any category where we have a covering class.

In [4], coGalois groups are studied in the category of representation of quiver .

We talk about the necessary conditions, give in [4], the coGalois group, associated to torsion free-cover, for an object in .

**References**

[1] E. Enochs: Torsion-free covering modules. (1963)

[2] E. Enochs, J. R. García Rozas and L. Oyonarte: Compact coGalois groups. (2000).

[3] E. Enochs and J. Rada: Abelian groups which have trivial absolute \ coGalois group. (2005).

[4] Paul Hill, Abelian group pairs having a trivial coGalois Group. (2006).