One-dimensional symmetry group

A one-dimensional symmetry group refers to a group of symmetries that act on a one-dimensional space, such as a line or an interval. In mathematical terms, this involves transformations that preserve certain properties of the space, specifically geometric or algebraic structures. ### Characteristics of One-Dimensional Symmetry Groups: 1. **Transformations**: The transformations in one-dimensional symmetry groups typically include translations, reflections, and rotations (though rotations in one dimension behave similarly to a reflection).