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- Primitive_permutation_group abstract "In mathematics, a permutation group G acting on a set X is called primitive if G acts transitively on X and G preserves no nontrivial partition of X. 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.In the same letter he stated also the following theorem.If G is a primitive solvable group acting on a finite set X, then the order of X is a power of a prime number p, X may be identified with an affine space over the finite field with p elements and G acts on X as a subgroup of the affine group.An imprimitive permutation group is an example of an induced representation; examples include coset representations G/H in cases where H is not a maximal subgroup. When H is maximal, the coset representation is primitive. If the set X is finite, its cardinality is called the "degree" of G. The numbers of primitive groups of small degree were stated by Robert Carmichael in 1937:Note the large number of primitive groups of degree 16. As Carmichael notes, all of these groups, except for the symmetric and alternating group, are subgroups of the affine group on the 4-dimensional space over the 2-element finite field. While primitive permutation groups are transitive by definition, not all transitive permutation groups are primitive. The requirement that a primitive group be transitive is necessary only when X is a 2-element set; otherwise, the condition that G preserves no nontrivial partition implies that G is transitive.".
- Primitive_permutation_group wikiPageExternalLink www.gap-system.org.
- Primitive_permutation_group wikiPageExternalLink prim.html.
- Primitive_permutation_group wikiPageID "2739252".
- Primitive_permutation_group wikiPageLength "4168".
- Primitive_permutation_group wikiPageOutDegree "30".
- Primitive_permutation_group wikiPageRevisionID "651647456".
- Primitive_permutation_group wikiPageWikiLink Affine_group.
- Primitive_permutation_group wikiPageWikiLink Affine_space.
- Primitive_permutation_group wikiPageWikiLink Alternating_group.
- Primitive_permutation_group wikiPageWikiLink Block_(permutation_group_theory).
- Primitive_permutation_group wikiPageWikiLink Category:Integer_sequences.
- Primitive_permutation_group wikiPageWikiLink Category:Permutation_groups.
- Primitive_permutation_group wikiPageWikiLink Coset.
- Primitive_permutation_group wikiPageWikiLink Finite_field.
- Primitive_permutation_group wikiPageWikiLink Galois_group.
- Primitive_permutation_group wikiPageWikiLink Group_action.
- Primitive_permutation_group wikiPageWikiLink Induced_representation.
- Primitive_permutation_group wikiPageWikiLink Jordans_theorem_(symmetric_group).
- Primitive_permutation_group wikiPageWikiLink Journal_of_Algebra.
- Primitive_permutation_group wikiPageWikiLink Mathematics.
- Primitive_permutation_group wikiPageWikiLink Maximal_subgroup.
- Primitive_permutation_group wikiPageWikiLink OEIS.
- Primitive_permutation_group wikiPageWikiLink On-Line_Encyclopedia_of_Integer_Sequences.
- Primitive_permutation_group wikiPageWikiLink Partition_of_a_set.
- Primitive_permutation_group wikiPageWikiLink Permutation_group.
- Primitive_permutation_group wikiPageWikiLink Prime_number.
- Primitive_permutation_group wikiPageWikiLink Robert_Carmichael.
- Primitive_permutation_group wikiPageWikiLink Robert_Daniel_Carmichael.
- Primitive_permutation_group wikiPageWikiLink Solvable_group.
- Primitive_permutation_group wikiPageWikiLink Symmetric_group.
- Primitive_permutation_group wikiPageWikiLink Évariste_Galois.
- Primitive_permutation_group wikiPageWikiLinkText "Primitive permutation group".
- Primitive_permutation_group wikiPageWikiLinkText "primitive permutation group".
- Primitive_permutation_group wikiPageWikiLinkText "primitive".
- Primitive_permutation_group wikiPageWikiLinkText "primitively".
- Primitive_permutation_group author "Todd Rowland".
- Primitive_permutation_group hasPhotoCollection Primitive_permutation_group.
- Primitive_permutation_group title "Primitive Group Action".
- Primitive_permutation_group urlname "PrimitiveGroupAction".
- Primitive_permutation_group wikiPageUsesTemplate Template:MathWorld.
- Primitive_permutation_group wikiPageUsesTemplate Template:OEIS_link.
- Primitive_permutation_group wikiPageUsesTemplate Template:Reflist.
- Primitive_permutation_group subject Category:Integer_sequences.
- Primitive_permutation_group subject Category:Permutation_groups.
- Primitive_permutation_group hypernym G.
- Primitive_permutation_group type Device.
- Primitive_permutation_group type Combinatoric.
- Primitive_permutation_group type Integer.
- Primitive_permutation_group comment "In mathematics, a permutation group G acting on a set X is called primitive if G acts transitively on X and G preserves no nontrivial partition of X. Otherwise, if G is transitive and G does preserve a nontrivial partition, G is called imprimitive.".
- Primitive_permutation_group label "Primitive permutation group".
- Primitive_permutation_group sameAs פעולה_פרימיטיבית.
- Primitive_permutation_group sameAs m.0803zl.
- Primitive_permutation_group sameAs Q7243579.
- Primitive_permutation_group sameAs Q7243579.
- Primitive_permutation_group wasDerivedFrom Primitive_permutation_group?oldid=651647456.
- Primitive_permutation_group isPrimaryTopicOf Primitive_permutation_group.