Definition:Transversal (Group Theory)/Left Transversal
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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.
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 6.3$. Index. Transversals
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): transversal: 2.