Remarks on commutators in finite groups
Let $G$ be a finite group and let $C = \{[x, y]\mid x, y\in G\}$ be the set of all the commutators in $G$. In general, $C < G^\prime$, where $G^\prime$ is the the commutator subgroup of $G$. In this paper, the authors give a interesting formula for the number $|H \backslash C|$ whenever $H$ is a normal subgroup of $G$. The number $|G\backslash C|$ is derived as a direct consequence.
scientific article; zbMATH DE number 6801929