About: Primitive permutation group

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In mathematics, a permutation group G acting on a non-empty finite set X is called primitive if G acts transitively on X and the only partitions the G-action preserves are the trivial partitions into either a single set or into |X| singleton sets. Otherwise, if G is transitive and G does preserve a nontrivial partition, G is called imprimitive. This terminology was introduced by Évariste Galois in his last letter, in which he used the French term équation primitive for an equation whose Galois group is primitive.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Arrangement107938773 yago:Group100031264 yago:Ordering108456993 yago:WikicatIntegerSequences device yago:Sequence108459252 yago:Series108457976 yago:WikicatPermutationGroups
rdfs:label	Primitive permutation group (en)
rdfs:comment	In mathematics, a permutation group G acting on a non-empty finite set X is called primitive if G acts transitively on X and the only partitions the G-action preserves are the trivial partitions into either a single set or into \|X\| singleton sets. Otherwise, if G is transitive and G does preserve a nontrivial partition, G is called imprimitive. This terminology was introduced by Évariste Galois in his last letter, in which he used the French term équation primitive for an equation whose Galois group is primitive. (en)
dcterms:subject	Integer sequences Permutation groups
Wikipage page ID	2739252 (xsd:integer)
Wikipage revision ID	1057516065 (xsd:integer)
Link from a Wikipage to another Wikipage	O'Nan–Scott theorem Trivial group Coset Mathematics Colva Roney-Dougal Évariste Galois Journal of Algebra Maximal subgroup Galois group Jordan's theorem (symmetric group) Affine group Affine space Alternating group Integer sequences Finite field Partition of a set Group action Prime number Abel–Ruffini theorem Permutation groups Block (permutation group theory) Induced representation OEIS Orbit (group theory) Klein four-group Solvable group Symmetric group Permutation group Transitive action Robert Carmichael
Link from a Wikipage to an external page	http://www.gap-system.org http://www.gap-system.org/Datalib/prim.html
sameAs	Primitive permutation group Primitive permutation group Primitive permutation group Primitive permutation group Primitive permutation group
dbp:wikiPageUsesTemplate	dbt:OEIS_link dbt:MathWorld dbt:Mvar dbt:Reflist dbt:Short_description dbt:Pages%3F
author	Todd Rowland (en)
title	Primitive Group Action (en)
urlname	PrimitiveGroupAction (en)
has abstract	In mathematics, a permutation group G acting on a non-empty finite set X is called primitive if G acts transitively on X and the only partitions the G-action preserves are the trivial partitions into either a single set or into \|X\| singleton sets. Otherwise, if G is transitive and G does preserve a nontrivial partition, G is called imprimitive. While primitive permutation groups are transitive, not all transitive permutation groups are primitive. The simplest example is the Klein four-group acting on the vertices of a square, which preserves the partition into diagonals. On the other hand, if a permutation group preserves only trivial partitions, it is transitive, except in the case of the trivial group acting on a 2-element set. This is because for a non-transitive action, either the orbits of G form a nontrivial partition preserved by G, or the group action is trivial, in which case all nontrivial partitions of X (which exists for \|X\| ≥ 3) are preserved by G. This terminology was introduced by Évariste Galois in his last letter, in which he used the French term équation primitive for an equation whose Galois group is primitive. (en)
gold:hypernym	G
prov:wasDerivedFrom	wikipedia-en:Primitive_permutation_group?oldid=1057516065&ns=0
page length (characters) of wiki page	6276 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Primitive_permutation_group
is Link from a Wikipage to another Wikipage of	System of imprimitivity List of permutation topics O'Nan–Scott theorem 110-vertex Iofinova-Ivanov graph Hall plane Mathieu group M12 Jordan's theorem (symmetric group) History of group theory Primitive Cheryl Praeger Block (permutation group theory) Sims conjecture Imprimitive Imprimitive group Primitive group Primitive permutation representation
is Wikipage redirect of	Imprimitive Imprimitive group Primitive group Primitive permutation representation
is Wikipage disambiguates of	Primitive
is foaf:primaryTopic of	wikipedia-en:Primitive_permutation_group

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