# Definition:Transversal (Group Theory)/Left Transversal

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## 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 $G$ if and only if every left coset of $H$ contains exactly one element of $S$.

## Also known as

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