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单词 PrimitivePermutationGroup
释义

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 (http://planetmath.org/BlockSystem).

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.

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更新时间:2025/5/4 15:15:37