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- Artin_transfer_(group_theory) abstract "In the mathematical field of group theory, an Artin transfer is a certain homomorphism from a group to the commutator quotient group of a subgroup of finite index.Originally, such mappings arose as group theoretic counterparts of class extension homomorphisms of abelian extensions of algebraic number fields by applying Artin's reciprocity maps to ideal class groups and analyzing the resulting homomorphisms between quotients of Galois groups.However, independently of number theoretic applications, the kernels and targets of Artin transfers have recently turned out to be compatible with parent-descendant relations between finite p-groups, which can be visualized in descendant trees. Therefore, Artin transfers provide a valuable tool for the classification of finite p-groups and for searching particular groups in descendant trees by looking for patterns defined by the kernels and targets of Artin transfers. These methods of pattern recognition are useful in purely group theoretic context, as well as for applications in algebraic number theory concerning higher p-class groups and Hilbert p-class field towers.".
- Artin_transfer_(group_theory) wikiPageExternalLink A242863.
- Artin_transfer_(group_theory) wikiPageExternalLink A242873.
- Artin_transfer_(group_theory) wikiPageExternalLink A242878.
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- Artin_transfer_(group_theory) wikiPageExternalLink A247689.
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- Artin_transfer_(group_theory) wikiPageExternalLink A247694.
- Artin_transfer_(group_theory) wikiPageExternalLink A247695.
- Artin_transfer_(group_theory) wikiPageExternalLink A247696.
- Artin_transfer_(group_theory) wikiPageExternalLink A247697.
- Artin_transfer_(group_theory) wikiPageID "43066470".
- Artin_transfer_(group_theory) wikiPageLength "121942".
- Artin_transfer_(group_theory) wikiPageOutDegree "50".
- Artin_transfer_(group_theory) wikiPageRevisionID "671388154".
- Artin_transfer_(group_theory) wikiPageWikiLink Abelianization.
- Artin_transfer_(group_theory) wikiPageWikiLink Algebraic_number_field.
- Artin_transfer_(group_theory) wikiPageWikiLink Algebraic_number_theory.
- Artin_transfer_(group_theory) wikiPageWikiLink Artin_reciprocity_law.
- Artin_transfer_(group_theory) wikiPageWikiLink Artin_transfer_(group_theory).
- Artin_transfer_(group_theory) wikiPageWikiLink Category:Class_field_theory.
- Artin_transfer_(group_theory) wikiPageWikiLink Category:Group_theory.
- Artin_transfer_(group_theory) wikiPageWikiLink Class_field_theory.
- Artin_transfer_(group_theory) wikiPageWikiLink Commutator_subgroup.
- Artin_transfer_(group_theory) wikiPageWikiLink Descendant_tree_(group_theory).
- Artin_transfer_(group_theory) wikiPageWikiLink Double_coset.
- Artin_transfer_(group_theory) wikiPageWikiLink File:Coclass1Tree2Groups.png.
- Artin_transfer_(group_theory) wikiPageWikiLink File:Coclass1Tree3Groups.png.
- Artin_transfer_(group_theory) wikiPageWikiLink File:Coclass1Tree5Groups.png.
- Artin_transfer_(group_theory) wikiPageWikiLink File:Coclass2TreeQType33.png.
- Artin_transfer_(group_theory) wikiPageWikiLink File:Coclass2TreeUType33.png.
- Artin_transfer_(group_theory) wikiPageWikiLink File:EpiAndArtinTransfers.png.
- Artin_transfer_(group_theory) wikiPageWikiLink File:EpiAndDerivedQuotients.png.
- Artin_transfer_(group_theory) wikiPageWikiLink File:FactorThruDerivedQuotient.png.
- Artin_transfer_(group_theory) wikiPageWikiLink File:FrequencyCoclass2Type33Sporadic.tiff.
- Artin_transfer_(group_theory) wikiPageWikiLink File:MinDiscriminantsCoclass2Type33Sporadic.tiff.
- Artin_transfer_(group_theory) wikiPageWikiLink File:MinDiscriminantsCoclass2Type55Sporadic.png.
- Artin_transfer_(group_theory) wikiPageWikiLink File:MinDiscriminantsCoclass2Type77Sporadic.tiff.
- Artin_transfer_(group_theory) wikiPageWikiLink File:MinDiscriminantsTreeQ.png.
- Artin_transfer_(group_theory) wikiPageWikiLink File:MinDiscriminantsTreeU.png.
- Artin_transfer_(group_theory) wikiPageWikiLink File:TreeCoclass2RootQ.png.
- Artin_transfer_(group_theory) wikiPageWikiLink Group_theory.
- Artin_transfer_(group_theory) wikiPageWikiLink P-group.
- Artin_transfer_(group_theory) wikiPageWikiLink P-group_generation_algorithm.
- Artin_transfer_(group_theory) wikiPageWikiLink Principalization_(algebra).
- Artin_transfer_(group_theory) wikiPageWikiLink Transfer_(group_theory).
- Artin_transfer_(group_theory) wikiPageWikiLinkText "'''induced automorphism'''".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "Artin transfer homomorphisms".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "Artin transfer".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "Artin transfers".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "commutator calculus".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "computational implementation".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "disjoint cycles".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "induced Artin transfer".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "induced transfer".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "kernels and targets of Artin transfers".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "pattern recognition".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "permutation representation".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "representatives".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "stabilization phenomena".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "straightforward".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "structured descendant trees".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "target of the Artin transfer".
- Artin_transfer_(group_theory) wikiPageWikiLinkText "transfer homomorphism".
- Artin_transfer_(group_theory) hasPhotoCollection Artin_transfer_(group_theory).
- Artin_transfer_(group_theory) wikiPageUsesTemplate Template:EquationNote.
- Artin_transfer_(group_theory) wikiPageUsesTemplate Template:Merge.
- Artin_transfer_(group_theory) wikiPageUsesTemplate Template:Multiple_issues.
- Artin_transfer_(group_theory) wikiPageUsesTemplate Template:Reflist.
- Artin_transfer_(group_theory) subject Category:Class_field_theory.
- Artin_transfer_(group_theory) subject Category:Group_theory.
- Artin_transfer_(group_theory) hypernym Homomorphism.
- Artin_transfer_(group_theory) comment "In the mathematical field of group theory, an Artin transfer is a certain homomorphism from a group to the commutator quotient group of a subgroup of finite index.Originally, such mappings arose as group theoretic counterparts of class extension homomorphisms of abelian extensions of algebraic number fields by applying Artin's reciprocity maps to ideal class groups and analyzing the resulting homomorphisms between quotients of Galois groups.However, independently of number theoretic applications, the kernels and targets of Artin transfers have recently turned out to be compatible with parent-descendant relations between finite p-groups, which can be visualized in descendant trees. ".
- Artin_transfer_(group_theory) label "Artin transfer (group theory)".
- Artin_transfer_(group_theory) sameAs m.010xbmrn.
- Artin_transfer_(group_theory) sameAs Q18354462.
- Artin_transfer_(group_theory) sameAs Q18354462.
- Artin_transfer_(group_theory) wasDerivedFrom Artin_transfer_(group_theory)?oldid=671388154.
- Artin_transfer_(group_theory) isPrimaryTopicOf Artin_transfer_(group_theory).