SQ-universal group

The concept of an SQ-universal group arises in the context of group theory and, more generally, plays a role in the study of model theory and the interplay between algebra and logic. An **SQ-universal group** is a type of group that satisfies certain properties with respect to a specific class of groups known as **SQ** (stable, quotient) groups. The term "universal" indicates that this group can realize all finite SQ-types over the empty set.