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The query [[Proves property satisfaction of::Self-centralizing subgroup]] was answered by the SMWSQLStore3 in 0.0040 seconds.


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 UsesFact about
Abelian permutable complement to core-free subgroup is-self-centralizingSelf-centralizing subgroup (?)
Central product decomposition lemma for characteristic rank oneCharacteristic rank one is characteristic subgroup-closed
Characteristic rank one implies cyclic-center
Extraspecial commutator-in-center subgroup is central factor
Self-centralizing subgroup (?)
Diagonal subgroup is self-centralizing in general linear groupSelf-centralizing subgroup (?)
Maximal among abelian normal implies self-centralizing in nilpotentNilpotent group (?)
Maximal among abelian normal subgroups (?)
Self-centralizing subgroup (?)
Maximal among Abelian normal subgroups of nilpotent group (2)
Self-centralizing subgroup of nilpotent group (3)
Maximal among abelian normal implies self-centralizing in supersolvableNormality is centralizer-closed
Normality satisfies image condition
Supersolvability is quotient-closed
Supersolvable implies every nontrivial normal subgroup contains a cyclic normal subgroup
Normality satisfies inverse image condition
Cyclic over central implies abelian
Supersolvable group (?)
Maximal among abelian normal subgroups (?)
Self-centralizing subgroup (?)
Maximal among abelian normal subgroups of supersolvable group (2)
Self-centralizing subgroup of supersolvable group (3)
Pi-separable and pi'-core-free implies pi-core is self-centralizingPi-separability is subgroup-closed
Characteristicity is centralizer-closed
Normality satisfies transfer condition
Characteristicity is transitive
Characteristic implies normal
Normal Hall implies permutably complemented
Normality satisfies intermediate subgroup condition
Cocentral implies normal
Equivalence of definitions of normal Hall subgroup
Self-centralizing subgroup (?)
Pi-separable group (?)
Solvable implies Fitting subgroup is self-centralizingCharacteristicity is centralizer-closed
Characteristicity is strongly intersection-closed
Solvable group (3)
Fitting subgroup (2)
Self-centralizing subgroup (2)
Self-centralizing subgroup (?)
Thompson's critical subgroup theoremMaximal among abelian normal implies self-centralizing in nilpotent
Characteristic and self-centralizing implies coprime automorphism-faithful
Normality satisfies image condition
Normality satisfies inverse image condition
Normality is centralizer-closed
Characteristic implies normal
Characteristicity is quotient-transitive
Characteristicity is transitive
Characteristicity is strongly intersection-closed
Characteristicity is centralizer-closed
Omega-1 of center is normality-large in nilpotent p-group
Self-centralizing subgroup (?)
Coprime automorphism-faithful subgroup (?)
Frattini-in-center group (2)
Commutator-in-center subgroup (1)
Self-centralizing subgroup (2)
Coprime automorphism-faithful subgroup (2)