primitive permutation group

Let X be a set, and G a transitiveMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath permutation groupMathworldPlanetmath on X. Then G is said to be a primitive permutation group if it has no nontrivial blocks (

For example, the symmetric groupMathworldPlanetmathPlanetmath S4 is a primitive permutation group on {1,2,3,4}.

Note that D8 is not a primitive permutation group on the vertices of a square, because the pairs of opposite points form a nontrivial block.

It can be shown that a transitive permutation group G on a set X is primitive if and only if the stabilizerMathworldPlanetmath StabG(x) is a maximal subgroup of G for all xX.

Title primitive permutation group
Canonical name PrimitivePermutationGroup
Date of creation 2013-03-22 14:00:49
Last modified on 2013-03-22 14:00:49
Owner Thomas Heye (1234)
Last modified by Thomas Heye (1234)
Numerical id 20
Author Thomas Heye (1234)
Entry type Definition
Classification msc 20B15