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The query [[Fact about.Page::Characteristic subgroup]] was answered by the SMWSQLStore3 in 0.0146 seconds.


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 UsesFact about
AEP upper-hook characteristic implies AEPAEP-subgroup (?)
Characteristic subgroup (?)
Additive group of a field implies characteristic in holomorphAdditive group of a field implies monolith in holomorph
Monolith is characteristic
Additive group of a field (2)
Holomorph-characteristic group (2)
Additive group of a field (?)
Characteristically simple group (?)
Elementary abelian group (?)
Characteristic subgroup (?)
Holomorph of a group (?)
Analogue of critical subgroup theorem for finite solvable groupsFinite solvable group (?)
Characteristic subgroup (?)
Frattini-in-center group (?)
Self-centralizing subgroup (?)
Coprime automorphism-faithful subgroup (?)
Center is characteristicCenter (1)
Characteristic subgroup (2)
Centerless and characteristic in automorphism group implies automorphism group is completeCenterless implies inner automorphism group is centralizer-free in automorphism group
Inner automorphism group is normal in automorphism group
Normal and centralizer-free implies automorphism-faithful
Automorphism group action lemma
Centerless group (?)
Automorphism group of a group (?)
Characteristic subgroup (?)
Complete group (?)
Characteristic and self-centralizing implies coprime automorphism-faithfulSelf-centralizing characteristic subgroup (2)
Coprime automorphism-faithful subgroup (2)
Characteristic subgroup (?)
Self-centralizing subgroup (?)
Coprime automorphism-faithful characteristic subgroup (?)
Characteristic central factor of WNSCDIN implies WNSCDINCharacteristic of normal implies normalComposition operator (?)
Characteristic central factor (?)
WNSCDIN-subgroup (?)
Characteristic central factor (2)
Left-transitively WNSCDIN-subgroup (2)
Characteristic subgroup (?)
Central factor (?)
Characteristic equals fully invariant in odd-order abelian groupOdd-order abelian group (?)
Characteristic subgroup (?)
Fully invariant subgroup (?)
Characteristic subgroup of odd-order abelian group (2)
Fully invariant subgroup of odd-order abelian group (3)
Characteristic equals strictly characteristic in HopfianHopfian group (?)
Characteristic subgroup (?)
Strictly characteristic subgroup (?)
Characteristic subgroup of Hopfian group (2)
Strictly characteristic subgroup of Hopfian group (3)
Characteristic equals verbal in free abelian groupFree abelian group (?)
Characteristic subgroup (?)
Verbal subgroup (?)
Characteristic subgroup of free abelian group (2)
Verbal subgroup of free abelian group (3)
Characteristic implies automorph-conjugateCharacteristic subgroup (2)
Automorph-conjugate subgroup (2)
Characteristic implies normalGroup acts as automorphisms by conjugationCharacteristic subgroup (1)
Normal subgroup (1)
Characteristic maximal subgroups may be isomorphic and distinct in group of prime power orderCharacteristic subgroup (?)
Maximal subgroup of group of prime power order (?)
Series-equivalent subgroups (?)
Characteristic not implies amalgam-characteristicCharacteristic subgroup (2)
Amalgam-characteristic subgroup (1)
Characteristic not implies characteristic-isomorph-free in finiteCharacteristic subgroup (2)
Characteristic-isomorph-free subgroup (2)
Characteristic not implies direct factorCharacteristic subgroup (2)
Direct factor (2)
Characteristic not implies elementarily characteristicCharacteristic subgroup (2)
Elementarily characteristic subgroup (2)
Characteristic not implies fully invariantCharacteristic subgroup (1)
Fully invariant subgroup (1)
Characteristic not implies fully invariant in class three maximal class p-groupMaximal class group (?)
Characteristic subgroup (?)
Fully invariant subgroup (?)
Characteristic not implies fully invariant in finite abelian groupFinite abelian group (2)
Characteristic subgroup (2)
Fully invariant subgroup (2)
Characteristic not implies fully invariant in finitely generated abelian groupFinitely generated abelian group (2)
Characteristic subgroup (2)
Fully invariant subgroup (2)
Characteristic not implies fully invariant in odd-order class two p-groupOdd-order class two p-group (2)
Characteristic subgroup (2)
Fully invariant subgroup (2)
Characteristic not implies injective endomorphism-invariantFinitary symmetric group is characteristic in symmetric group
Finitary symmetric group is not injective endomorphism-invariant in symmetric group
Center is characteristic
Center not is injective endomorphism-invariant
Characteristic subgroup (2)
Injective endomorphism-invariant subgroup (2)
Characteristic not implies injective endomorphism-invariant in finitely generated abelian groupFinitely generated abelian group (2)
Characteristic subgroup (2)
Injective endomorphism-invariant subgroup (2)
Characteristic not implies isomorph-free in finite groupFinite group (2)
Characteristic subgroup (2)
Isomorph-free subgroup (2)
Characteristic not implies isomorph-normal in finite groupFinite group (2)
Characteristic subgroup (2)
Isomorph-normal subgroup (2)
Characteristic not implies normal-isomorph-freeCharacteristic not implies characteristic-isomorph-free in finite
Normal-isomorph-free implies characteristic-isomorph-free
Characteristic-isomorph-free not implies normal-isomorph-free in finite
Characteristic-isomorph-free implies characteristic
Series-equivalent characteristic subgroups may be distinct
Normal-isomorph-free implies series-isomorph-free
Finite group (2)
Characteristic subgroup (2)
Normal-isomorph-free subgroup (2)
Characteristic not implies potentially fully invariantNormal not implies potentially fully invariant
Normal equals potentially characteristic
Characteristic subgroup (2)
Potentially fully invariant subgroup (2)
Characteristic not implies powering-invariant in solvable groupSolvable group (2)
Characteristic subgroup (2)
Powering-invariant subgroup (2)
Characteristic not implies quasiautomorphism-invariantCharacteristic subgroup (2)
Quasiautomorphism-invariant subgroup (2)
Characteristic not implies strictly characteristicCharacteristic subgroup (2)
Strictly characteristic subgroup (2)
Characteristic not implies sub-(isomorph-normal characteristic) in finiteFinite group (2)
Characteristic subgroup (2)
Sub-(isomorph-normal characteristic) subgroup (2)
Characteristic not implies sub-isomorph-free in finite groupFinite group (2)
Characteristic subgroup (2)
Sub-isomorph-free subgroup (2)
Characteristic of CDIN implies CDINComposition operator (?)
Characteristic subgroup (?)
CDIN-subgroup (?)
Characteristic subgroup (2)
Left-transitively CDIN-subgroup (2)
Characteristic of normal implies normalRestriction of automorphism to subgroup invariant under it and its inverse is automorphism
Composition rule for function restriction
Composition operator (?)
Characteristic subgroup (?)
Normal subgroup (?)
Characteristic of potentially characteristic implies potentially characteristicComposition operator (?)
Characteristic subgroup (?)
Potentially characteristic subgroup (?)
Characteristic subgroup of Sylow subgroup is weakly closed iff it is normal in every Sylow subgroup containing itWeakly closed implies conjugation-invariantly relatively normal in finite group
Sylow implies order-conjugate
Sylow implies WNSCDIN
WNSCDIN implies every normalizer-relatively normal conjugation-invariantly relatively normal subgroup is weakly closed
Sylow subgroup (?)
Characteristic subgroup (?)
Weakly closed subgroup (?)
Characteristic subgroup of abelian group not implies divisibility-closedCharacteristic subgroup of abelian group (2)
Divisibility-closed subgroup (2)
Abelian group (2)
Characteristic subgroup (2)
Characteristic subgroup of abelian group not implies local powering-invariantCharacteristic subgroup of abelian group (2)
Local powering-invariant subgroup (2)
Abelian group (2)
Characteristic subgroup (2)
Characteristic subgroup of additive group of odd-order Lie ring is derivation-invariant and fully invariantCharacteristic equals fully invariant in odd-order abelian group
Fully invariant subgroup of additive group of Lie ring is derivation-invariant and fully invariant
Characteristic subgroup (?)
Derivation-invariant Lie subring (?)
Ideal of a Lie ring (?)
Fully invariant Lie subring (?)
Characteristic subgroup of uniquely p-divisible abelian group is uniquely p-divisibleAbelian implies uniquely p-divisible iff pth power map is automorphismAbelian group (?)
Characteristic subgroup (?)
Powered group for a set of primes (?)
Characteristic subset generates characteristic subgroupCharacteristic subset of a group (1)
Characteristic subgroup (3)
Characteristic upper-hook AEP implies characteristicAEP-subgroup (2)
Subgroup in which every subgroup characteristic in the whole group is characteristic (2)
Characteristic subgroup (?)
AEP-subgroup (?)
Characteristicity does not satisfy image conditionCharacteristic subgroup (1)
Image condition (2)
Characteristicity does not satisfy intermediate subgroup conditionCharacteristic subgroup (1)
Intermediate subgroup condition (2)
Characteristicity does not satisfy lower central series conditionCharacteristic subgroup (1)
Lower central series condition (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 not finite direct power-closedCharacteristic subgroup (1)
Finite direct power-closed subgroup property (2)
Characteristicity is not finite-relative-intersection-closedCharacteristic subgroup (1)
Finite-relative-intersection-closed subgroup property (2)