Transversal (combinatorics): Difference between revisions

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==Examples==

In Euclidean 3-space, a [[regulus (geometry)|regulus]] is a pairset of sets[[skew madelines]], up{{mvar|R}}, such that through each point on each line of opposite{{mvar|R}}, there passes a transversal of {{mvar|R}} and through each point of a transversal of {{mvar|R}} there passes a line of {{mvar|R}}. The set of transversals of a regulus {{mvar|R}} is also a regulus, called the ''opposite regulus''.

In [[group theory]], given a [[subgroup]] ''H'' of a group ''G'', a right (respectively left) transversal is a [[Set (mathematics)|set]] containing exactly one element from each right (respectively left) [[coset]] of ''H''. In this case, the "sets" (cosets) are mutually disjoint, i.e. the cosets form a [[Partition of a set|partition]] of the group.