On coGalois Groups III

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 \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 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 q_2 : \cdot \rightarrow \cdot . We talk about the necessary and sufficient conditions for coGalois group, associated to a torsion free-cover of an object in (q_2, Z-mod) 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