# Definition:Transversal (Group Theory)/Right 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 right transversal for $H$ in $G$ if and only if every right coset of $H$ contains exactly one element of $S$.

## Also known as

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