automorphism groups

An automorphism group is a mathematical concept that describes a set of symmetries of a structure that maps the structure onto itself without changing its essential properties. For example, consider a geometric shape; an automorphism would be a rotation or reflection that leaves the shape looking the same. The group aspect refers to the collection of all these symmetries combined, where you can perform one after another and still stay within the set of symmetries. This concept helps mathematicians understand and classify structures in various fields, such as algebra, geometry, and even networks.