Abstract: 

This talk explores the structural and model-theoretic properties of Abelian groups, beginning with an analysis of direct products. We will examine the construction of ultraproducts and distinguish their algebraic behavior from standard direct sums. A significant portion of the discussion will focus on pseudofiniteness and how infinite groups can retain first-order properties of finite structures. Furthermore, we will discuss the concept of absorbing groups and their significance in the theory. The talk aims to provide a clear overview of the interplay between these algebraic constructions and logical frameworks. This is joint work with Nurlan Markhabatov.