# Category:Transversals

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This category contains results about Transversals in the context of Group Theory.

Definitions specific to this category can be found in Definitions/Transversals.

Let $G$ be a group.

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

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

### Left Transversal

$S$ is a **left transversal for $H$ in $G$** if and only if every left coset of $H$ contains **exactly one** element of $S$.

### Right Transversal

$S$ is a **right transversal for $H$ in $G$** if and only if every right coset of $H$ contains **exactly one** element of $S$.

### Transversal

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

## Pages in category "Transversals"

The following 2 pages are in this category, out of 2 total.