On coGalois Groups – Dokuz Eylül University Faculty of Science Department of Mathematics

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 $\phi: T \rightarrow A$ of an abelian group is defined in [2] as the group of $f: T \rightarrow T$ s.t. $\phi f= \phi$ and is denoted by $G(\phi)$ .
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 $q_2 : \cdot \rightarrow \cdot$ .
We talk about the necessary conditions, give in [4], the coGalois group, associated to torsion free-cover, for an object in $(q_2, Z-mod)$ .

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).