Group Automorphism/Examples
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Examples of Group Automorphisms
Constant Product on Real Numbers
Let $\struct {\R, +}$ denote the real numbers under addition.
Let $\alpha \in \R$ be a real number.
Let $f: \R \to \R$ be the real function defined as:
- $\forall x \in \R: \map f x = \alpha x$
Then $f$ is a (group) automorphism if and only if $\alpha \ne 0$.