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 $\alpha \ne 0$.