Solution
= Solution
The <identity element> satisfies $e*x=exe^{-1}=x$. For $g,h\in G$,
$$
(gh)*x=ghxh^{-1}g^{-1}=g*(h*x).
$$
Both <action> axioms hold, so \b[<conjugation> is a <group action> on $G$].
= Solution
The <identity element> satisfies $e*x=exe^{-1}=x$. For $g,h\in G$,
$$
(gh)*x=ghxh^{-1}g^{-1}=g*(h*x).
$$
Both <action> axioms hold, so \b[<conjugation> is a <group action> on $G$].