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The query [[Proves property satisfaction of::Characteristic subgroup]] was answered by the SMWSQLStore3 in 0.0112 seconds.

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 UsesFact about
Center is characteristicCenter (1)
Characteristic subgroup (2)
Characteristicity is centralizer-closedCharacteristic subgroup (1)
Centralizer-closed subgroup property (2)
Characteristicity is commutator-closedCharacteristic subgroup (1)
Commutator-closed subgroup property (2)
Characteristicity is strongly intersection-closedCharacteristic subgroup (1)
Strongly intersection-closed subgroup property (2)
Characteristicity is strongly join-closedCharacteristic subgroup (1)
Strongly join-closed subgroup property (2)
Characteristicity is transitiveCharacteristic subgroup (1)
Transitive subgroup property (2)
Cyclic subgroup is characteristic in dihedral groupCharacteristic subgroup (?)
Dihedral group (?)
Derived subgroup is characteristicSdf (1)
Property (2)
Every group is characteristic in itselfCharacteristic subgroup (1)
Identity-true subgroup property (2)
Finitary alternating group is characteristic in symmetric groupAlternating group (?)
Characteristic subgroup (?)
Symmetric group (?)
Finitary symmetric group is characteristic in symmetric groupFinitary alternating group is intermediately monolith in symmetric group
Monolith is characteristic
Finitary symmetric group equals center of symmetric group modulo finitary alternating group
Characteristicity is quotient-transitive		Finitary symmetric group (?)
Characteristic subgroup (?)
Symmetric group (?)
Fully invariant implies characteristicFully invariant subgroup (2)
Characteristic subgroup (2)
Isomorph-containing implies characteristicIsomorph-containing subgroup (2)
Characteristic subgroup (2)
Left-transitively complemented normal implies characteristicLeft residual of normal by complemented normal equals characteristicLeft-transitively complemented normal subgroup (2)
Characteristic subgroup (2)
Complemented characteristic subgroup (?)
Left-transitively permutable implies characteristicEvery group is normal fully normalized in its holomorphLeft-transitively permutable subgroup (2)
Characteristic subgroup (2)
Permutable subgroup (?)
Normality-preserving endomorphism-invariant implies characteristicAutomorphism implies normality-preserving endomorphismNormality-preserving endomorphism-invariant subgroup (2)
Characteristic subgroup (2)
Normality-preserving endomorphism (?)
Self-centralizing and minimal normal implies characteristicSelf-centralizing and minimal normal implies monolith
Monolith is characteristic		Self-centralizing minimal normal subgroup (2)
Characteristic subgroup (2)
Minimal normal subgroup (?)
Self-centralizing subgroup (?)
Special linear group is characteristic in general linear groupDerived subgroup of general linear group is special linear group
Commutator subgroup is characteristic		Special linear group (?)
Characteristic subgroup (?)
General linear group over a field (?)
Subgroup-defining function value is characteristic
Trivial subgroup is characteristicCharacteristic subgroup (1)
Trivially true subgroup property (2)
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