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The query [[Fact about.Page::Normal subgroup]] was answered by the SMWSQLStore3 in 0.0119 seconds.


Results 1 – 50    (Previous 50 | Next 50)   (20 | 50 | 100 | 250 | 500)   (JSON | CSV | RSS | RDF)
 Difficulty levelFact about
Automorph-join-closed subnormal of normal implies conjugate-join-closed subnormal1Composition operator (?)
Automorph-join-closed subnormal subgroup (?)
Normal subgroup (?)
Conjugate-join-closed subnormal subgroup (?)
Automorph-permutable of normal implies conjugate-permutable1Composition operator (?)
Automorph-permutable subgroup (?)
Normal subgroup (?)
Conjugate-permutable subgroup (?)
Bound on double coset index in terms of orders of group and subgroupDouble coset of a pair of subgroups (?)
Double coset index of a subgroup (?)
Subgroup of finite index (?)
Malnormal subgroup (?)
Normal subgroup (?)
Frobenius subgroup (?)
Cartan-Brauer-Hua theorem4Normal subgroup (?)
Division ring (?)
Central factor implies normalCentral factor (2)
Normal subgroup (2)
Central implies normal1Central subgroup (2)
Normal subgroup (2)
Characteristic implies normal1Characteristic subgroup (1)
Normal subgroup (1)
Characteristic of normal implies normal1Composition operator (?)
Characteristic subgroup (?)
Normal subgroup (?)
Commutator of a group and a subgroup implies normal3Commutator operator (3)
Improper subgroup (2)
Subgroup (2)
Normal subgroup (2)
Subgroup realizable as the commutator of the whole group and a subgroup (2)
Commutator of a group and a subset implies normal3Commutator operator (3)
Improper subgroup (2)
Subset of a group (2)
Normal subgroup (2)
Commutator of a normal subgroup and a subgroup not implies normalNormal subgroup (?)
Commutator of two subgroups (?)
Commutator of a normal subgroup and a subset implies 2-subnormalCommutator operator (3)
Normal subgroup (2)
Subset of a group (2)
2-subnormal subgroup (2)
Subgroup realizable as the commutator of a normal subgroup and a subset (2)
Comparable with all normal subgroups implies normal in nilpotent groupNilpotent group (?)
Subgroup comparable with all normal subgroups (?)
Normal subgroup (?)
Subgroup comparable with all normal subgroups of nilpotent group (2)
Normal subgroup of nilpotent group (3)
Composition of subgroup property satisfying intermediate subgroup condition with normality equals property in normal closureIntermediate subgroup condition (?)
Composition operator (?)
Normal subgroup (?)
Normal closure (?)
Conjugate-comparable not implies normalConjugate-comparable subgroup (2)
Normal subgroup (2)
Conjunction of normality with any nontrivial finite-direct product-closed property of groups is not transitiveFinite-direct product-closed group property (?)
Normal subgroup (?)
Direct factor implies normalDirect factor (2)
Normal subgroup (2)
Equivalence of conjugacy and commutator definitions of normality1Normal subgroup (1)
Equivalence of conjugacy and coset definitions of normality1Normal subgroup (1)
Normalizer of a subgroup (1)
Conjugate subgroups (?)
Left coset of a subgroup (?)
Normalizer of a subgroup (?)
Normal subgroup (?)
Every group is normal fully normalized in its holomorphHolomorph of a group (?)
Normal subgroup (?)
Fully normalized subgroup (?)
Every group is normal in itself0Normal subgroup (1)
Identity-true subgroup property (2)
Every nontrivial normal subgroup is potentially characteristic-and-not-fully invariantNormal subgroup (?)
Characteristic subgroup (?)
Fully invariant subgroup (?)
Every nontrivial normal subgroup is potentially characteristic-and-not-intermediately characteristicNormal subgroup (?)
Characteristic subgroup (?)
Every nontrivial normal subgroup is potentially normal-and-not-characteristicNormal subgroup (?)
Every subgroup is contracharacteristic in its normal closureComposition operator (?)
Contracharacteristic subgroup (?)
Normal subgroup (?)
Subgroup (?)
Extensible automorphism-invariant equals normalNormal subgroup (1)
Finitary symmetric group is normal in symmetric groupFinitary symmetric group (?)
Normal subgroup (?)
Symmetric group (?)
First isomorphism theorem2Normal subgroup (?)
Fourth isomorphism theorem2Normal subgroup (?)
Index three implies normal or double coset index twoSubgroup of index three (?)
Normal subgroup (?)
Subgroup of double coset index two (?)
Induced class function from normal subgroup is zero outside the subgroupNormal subgroup (?)
Class function (?)
Induced class function (?)
Inner automorphism to automorphism is right tight for normalityNormal subgroup (?)
Intermediately automorph-conjugate of normal implies weakly pronormalIntermediately automorph-conjugate subgroup of normal subgroup (2)
Weakly pronormal subgroup (2)
Intermediately automorph-conjugate subgroup (?)
Normal subgroup (?)
Intermediately isomorph-conjugate of normal implies pronormalIntermediately isomorph-conjugate subgroup of normal subgroup (2)
Pronormal subgroup (2)
Composition operator (?)
Intermediately isomorph-conjugate subgroup (?)
Normal subgroup (?)
Pronormal subgroup (?)
Intermediately normal-to-characteristic of normal implies intermediately subnormal-to-normalComposition operator (?)
Intermediately normal-to-characteristic subgroup (?)
Normal subgroup (?)
Intermediately subnormal-to-normal subgroup (?)
Join of normal and subnormal implies subnormal of same depthJoin operator (?)
Subgroup property (?)
Normal subgroup (?)
Subnormal subgroup (?)
Subnormal depth (2)
Join-transitively subnormal of normal implies finite-conjugate-join-closed subnormalComposition operator (?)
Join-transitively subnormal subgroup (?)
Normal subgroup (?)
Finite-conjugate-join-closed subnormal subgroup (?)
Left residual of 2-subnormal by normal is normal of characteristicNormal subgroup of characteristic subgroup (1)
Normal subgroup of characteristic subgroup (?)
Normal subgroup (?)
2-subnormal subgroup (?)
Left transiter of normal is characteristic3Characteristic subgroup (?)
Normal subgroup (?)
Left-transitively WNSCDIN not implies normalLeft-transitively WNSCDIN-subgroup (2)
Normal subgroup (2)
Maximal conjugate-permutable implies normalNormal subgroup (?)
Conjugate-permutable subgroup (?)
Maximal implies normal or abnormal2Maximal subgroup (?)
Normal subgroup (?)
Abnormal subgroup (?)
Maximal implies normal or self-normalizingMaximal subgroup (?)
Normal subgroup (?)
Self-normalizing subgroup (?)
Maximal permutable implies normalNormal subgroup (?)
Permutable subgroup (?)
Nilpotent implies every maximal subgroup is normalNilpotent group (?)
Maximal subgroup (?)
Normal subgroup (?)
Maximal subgroup of nilpotent group (2)
Normal subgroup of nilpotent group (3)
Group in which every maximal subgroup is normal (?)
Nilpotent implies every normal subgroup is potentially characteristicNilpotent group (?)
Normal subgroup (?)
Potentially characteristic subgroup (?)
Normal subgroup of nilpotent group (2)
Potentially characteristic subgroup of nilpotent group (3)
No subgroup property between normal Sylow and subnormal or between Sylow retract and retract is conditionally lattice-determinedSubnormal subgroup (1)
Conditionally lattice-determined subgroup property (2)
Normal subgroup (1)
Characteristic subgroup (1)
Fully invariant subgroup (1)
Normal Hall subgroup (1)
Normal Sylow subgroup (1)
Complemented normal subgroup (1)
Sylow retract (1)
Hall retract (1)
Retract (1)
Normal and self-centralizing implies coprime automorphism-faithfulSelf-centralizing normal subgroup (2)
Coprime automorphism-faithful normal subgroup (2)
Coprime automorphism group (?)
Normal subgroup (?)
Self-centralizing subgroup (?)
Coprime automorphism-faithful subgroup (?)
Normal and self-centralizing implies normality-largeSelf-centralizing normal subgroup (2)
Normality-large normal subgroup (2)
Normal subgroup (?)
Self-centralizing subgroup (?)
Normality-large subgroup (?)
Normal equals potentially characteristic3Normal subgroup (1)