Past exam of the mathematics course of the University of Oxford / 2014 / Prelims / Mathematics I / 6 / a / i / Solution

A subgroup $N$ of $G$ is a normal subgroup if conjugation by every element preserves it:Equivalently, $gN=Ng$ for every $g\in G$. Here equality means equality of sets; it does not require each individual element of $N$ to commute with every element of $G$.