Canan Özeren, Dokuz Eylül University.
Date: 12th of April, 2023, Wednesday,
Time: 10:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206 (Online-Sakai-Graduate Meetings).
Abstract:Torsion-free covers exist for abelian groups (see [1]). The coGalois group of a torsion-free cover
![Rendered by QuickLaTeX.com \phi: T \rightarrow A](https://quicklatex.com/cache3/fd/ql_dc0d1f58045e5e28f023cc07b46a8cfd_l3.png)
of an abelian group is defined in [2] as the group of
![Rendered by QuickLaTeX.com f: T \rightarrow T](https://quicklatex.com/cache3/22/ql_ca7b8a83aa35d6b4df4e5ecada1a4e22_l3.png)
s.t.
![Rendered by QuickLaTeX.com \phi f= \phi](https://quicklatex.com/cache3/4b/ql_0856c98026202f72123e2819a4d8af4b_l3.png)
and is denoted by
![Rendered by QuickLaTeX.com G(\phi)](https://quicklatex.com/cache3/3d/ql_041f44b26b24050f06f883f5a70ad63d_l3.png)
. The abelian groups for which the coGalois group is trivial were characterized in [3]. The notion of coGalois group can be defined in any category where we have a covering class. In [4], coGalois groups have been studied in the category of representations of the quiver
![Rendered by QuickLaTeX.com q_2 : \cdot \rightarrow \cdot](https://quicklatex.com/cache3/bf/ql_3d3f82673e851fcb4eaaa21bfa987ebf_l3.png)
. We talk about the necessary and sufficient conditions for coGalois group, associated to a torsion free-cover of an object in
![Rendered by QuickLaTeX.com (q_2, Z-mod)](https://quicklatex.com/cache3/cc/ql_1e766d473579cff75cfb954ed6a284cc_l3.png)
to be trivial.
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). [5] Molly Dukun, Phd Thesis
[5] Molly Dukun, Phd Thesis