= Power-map group action obstruction
{title2=$\rho(n,x)=x^n$}
Suppose a <binary operation> on the underlying <set> $\mathbb Z$ makes it a <group>, and $\rho(n,x)=x^n$ is a <group action> on another <group> $G$. Every acting element must induce a <bijection>, with <inverse function> given by its acting <inverse element>. The integer $0$ instead induces the constant <function> $x\mapsto e$, where $e$ is the <identity element> of $G$, so $G$ must be the <trivial group>. Conversely, on the <trivial group>, ordinary <addition> on $\mathbb Z$ supplies such a <group action>.
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