Definition:Transversal (Group Theory)/Right 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 right transversal for $H$ in $G$ if and only if every right coset of $H$ contains exactly one element of $S$.
Also known as
A right transversal is also known as a set of right coset representatives.
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 6.3$. Index. Transversals
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): $\S 3.3$: Group actions and coset decompositions
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): transversal: 2.