multiply transitive

Let G be a group, X a set on which it acts. Let X(n) be the set of order n-tuples of distinct elements of X. This is a G-set by the diagonal action:


The action of G on X is said to be n-transitiveMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath if it acts transitively on X(n).

For example, the standard action of Sn, the symmetric groupMathworldPlanetmathPlanetmath, is n-transitive, and the standard action of An, the alternating groupMathworldPlanetmath, is (n-2)-transitive.

Title multiply transitive
Canonical name MultiplyTransitive
Date of creation 2013-03-22 13:16:37
Last modified on 2013-03-22 13:16:37
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 5
Author bwebste (988)
Entry type Definition
Classification msc 20B20
Synonym n-transitive