Category:Definitions/Transversals (Group Theory)

This category contains definitions related to transversals in the context of group theory.
Related results can be found in Category:Transversals (Group Theory).

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.