noun
- plural of automorphism: mathematical transformations of a structure that preserve its essential properties and map the structure onto itself
Usage: mathematics; technical
Examples
- The group of automorphisms of a square includes rotations and reflections.
- Mathematicians study automorphisms to understand symmetries in algebraic structures.
- The automorphisms of this graph preserve all adjacency relationships.
- Ring automorphisms maintain both addition and multiplication operations.
- Field automorphisms are particularly important in Galois theory.
- The identity transformation is always included among the automorphisms of any structure.