Affine symmetric group

The affine symmetric group, often denoted as \( \text{Aff}(\mathbb{Z}/n\mathbb{Z}) \) or \( \text{Aff}(n) \), is an extension of the symmetric group that includes not only permutations of a finite set but also affine transformations. Specifically, it refers to a group of transformations that act on a finite cyclic group, typically represented as \( \mathbb{Z}/n\mathbb{Z} \).