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Characteristic subgroup

concept 1 articles 16 citations 18 shown relations

MathematicsAlgebra

, $\mathrm{Socl}(G)$, the layer, $E(G)$, and the generalized Fitting subgroup. For a definition of the last two, cf.

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A subgroup of a group $G$ that is invariant under all automorphisms of $G$.

Comments

Examples of characteristic subgroups are the centre of a group, denoted by $Z(G)$, the Fitting subgroup, $F(G)$, the commutator subgroup, $D(G)$, $[G,G]$ or $G'$, the Frattini subgroup, $\Phi(G)$, the socle, $\mathrm{Socl}(G)$, the layer, $E(G)$, and the generalized Fitting subgroup. For a definition of the last two, cf. Fitting subgroup.

How to Cite This Entry:
Characteristic subgroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Characteristic_subgroup&oldid=35104

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article

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AlgebraMathematics / Algebramethod: keyword_rule - confidence: 0.68suggested

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Characteristic subgroupencyclopedia_of_mathematics

Citations

Frattini subgroupoutgoing citation Automorphismoutgoing citation Centre of a groupoutgoing citation Socleoutgoing citation Commutator subgroupoutgoing citation Fitting subgroupoutgoing citation Fitting subgroupincoming citation Centre of a groupincoming citation Fitting chainincoming citation Socleincoming citation Thompson subgroupincoming citation Frattini-subgroup(2)incoming citation Regular p-groupincoming citation Normal subgroupincoming citation Subnormal seriesincoming citation Frattini subgroupincoming citation

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discussesarticle:eom--characteristic-subgroup--0d8fa2b2fb -> concept:characteristic-subgroupconfidence: 1.00 - provenance: encyclopedia_of_mathematicsconfirmed

citesconcept:characteristic-subgroup -> concept:frattini-subgroupconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:characteristic-subgroup -> concept:automorphismconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:characteristic-subgroup -> concept:centre-of-a-groupconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:characteristic-subgroup -> concept:socleconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:characteristic-subgroup -> concept:commutator-subgroupconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:characteristic-subgroup -> concept:fitting-subgroupconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:fitting-subgroup -> concept:characteristic-subgroupconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:centre-of-a-group -> concept:characteristic-subgroupconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:fitting-chain -> concept:characteristic-subgroupconfidence: 1.00 - provenance: article backlink extractionreviewed

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citesconcept:thompson-subgroup -> concept:characteristic-subgroupconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:frattini-subgroup-2 -> concept:characteristic-subgroupconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:regular-p-group -> concept:characteristic-subgroupconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:normal-subgroup -> concept:characteristic-subgroupconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:subnormal-series -> concept:characteristic-subgroupconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:frattini-subgroup -> concept:characteristic-subgroupconfidence: 1.00 - provenance: article backlink extractionreviewed

subcategory_ofconcept:characteristic-subgroup -> topic:algebraconfidence: 0.68 - provenance: keyword_rule classificationsuggested

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