Category:Definitions/Transversals

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