primitive permutation group
Let be a set, and a transitive permutation group
on .Then is said to be a primitive permutation group if it has no nontrivial blocks (http://planetmath.org/BlockSystem).
For example, the symmetric group is a primitive permutation group on .
Note that 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 on a set is primitive if and only if the stabilizer is a maximal subgroup of for all .