Definition:Transversal (Group Theory)

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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 $G$.

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

Clearly if $S$ is a transversal for $H$ it contains $\left[{G : H}\right]$ elements, where $\left[{G : H}\right]$ denotes the index of $H$ in $G$.