Definition:Automorphism Group
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Definition
Group of Automorphisms
Let $\struct {S, *}$ be an algebraic structure.
Let $\mathbb S$ be the set of automorphisms of $S$.
Then the algebraic structure $\struct {\mathbb S, \circ}$, where $\circ$ denotes composition of mappings, is called the automorphism group of $S$.
The structure $\struct {S, *}$ is usually a group. However, this is not necessary for this definition to be valid.
Also see
- Definition:Homeomorphism Group, which plays the role as the group of automorphisms of a topological space
- Definition:Galois Group of Field Extension
- Definition:Galois Group of Covering Map