Definition:Transversal (Group Theory)

Definition
Let $G$ be a group.

Let $H$ be a subgroup of $G$.

Let $S \subseteq G$ be a subset of $G$.

Transversal
A transversal for $H$ in $G$ is either a left transversal or a right transversal.

Clearly if $S$ is a transversal for $H$ it contains $\index G H$ elements, where $\index G H$ denotes the index of $H$ in $G$.