Definition:Transversal (Group Theory)/Left Transversal

Definition
Let $G$ be a group.

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

Let $S \subseteq G$ be a subset of $G$. $S$ is a left transversal for $H$ in $G$ iff every left coset of $H$ contains exactly one element of $S$.

A left transversal is also known as a set of left coset representatives.

Also see

 * Right Transversal