Retract (group theory)

In the context of group theory, a **retract** is a specific type of subgroup related to the notion of projection. To understand this concept, we first need to define a few key terms: 1. **Group**: A set equipped with an operation that satisfies four fundamental properties: closure, associativity, the identity element, and invertibility. 2. **Subgroup**: A subset of a group that itself forms a group under the operation of the larger group.