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The query [[Fact about.Page::Nilpotent group]] was answered by the SMWSQLStore3 in 0.0051 seconds.


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 Difficulty levelFact about
Abelian implies nilpotentAbelian group (2)
Nilpotent group (2)
Ambivalent and nilpotent implies 2-groupAmbivalent group (2)
Nilpotent group (3)
C-closed implies completely divisibility-closed in nilpotent groupNilpotent group (?)
C-closed subgroup (?)
Completely divisibility-closed subgroup (?)
C-closed subgroup of nilpotent group (2)
Completely divisibility-closed subgroup of nilpotent group (3)
CA not implies nilpotentCA-group (2)
Nilpotent group (2)
CN-group (2)
Abelian group (3)
Commutator-verbal implies divisibility-closed in nilpotent groupNilpotent group (?)
Commutator-verbal subgroup (?)
Divisibility-closed subgroup (?)
Commutator-verbal subgroup of nilpotent group (2)
Divisibility-closed subgroup of nilpotent group (3)
Commuting fraction more than half implies nilpotentCommuting fraction (2)
Nilpotent group (3)
Finite nilpotent group (3)
Number of conjugacy classes (3)
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)
Derived length gives no upper bound on nilpotency classNilpotent group (?)
Derived length (?)
Nilpotency class (?)
Derived length is logarithmically bounded by nilpotency classNilpotent group (3)
Nilpotency class (2)
Solvable group (3)
Derived length (2)
Derived subgroup not is intermediately powering-invariant in nilpotent groupNilpotent group (3)
Derived subgroup (2)
Intermediately powering-invariant subgroup (2)
Divisibility-closedness is strongly join-closed in nilpotent groupNilpotent group (?)
Divisibility-closed subgroup (?)
Strongly join-closed subgroup property (?)
Epicentral series members are completely divisibility-closed in nilpotent groupNilpotent group (3)
Epicentral series (3)
Completely divisibility-closed subgroup (3)
Epicenter (3)
Equivalence of definitions of nilpotent groupNilpotent group (1)
Equivalence of definitions of periodic nilpotent groupPeriodic nilpotent group (1)
Nilpotent group (2)
Periodic abelian group (2)
Restricted external direct product (2)
Nilpotent p-group (2)
Nilpotency class (2)
Finite non-nilpotent and every proper subgroup is nilpotent implies not simpleNilpotent group (3)
Finite nilpotent group (3)
Group with nilpotent derived subgroupDerived subgroup (?)
Nilpotent group (?)
Nilpotent normal subgroup (?)
Nilpotent characteristic subgroup (?)
Intermediately automorph-conjugate implies intermediately characteristic in nilpotentNilpotent group (?)
Intermediately automorph-conjugate subgroup (?)
Intermediately characteristic subgroup (?)
Intermediately automorph-conjugate subgroup of nilpotent group (2)
Intermediately characteristic subgroup of nilpotent group (3)
Intermediately normal-to-characteristic implies intermediately characteristic in nilpotentNilpotent group (?)
Intermediately normal-to-characteristic subgroup (?)
Intermediately characteristic subgroup (?)
Intermediately normal-to-characteristic subgroup of nilpotent group (2)
Intermediately characteristic subgroup of nilpotent group (3)
Isoclinic groups have same nilpotency classIsoclinic groups (?)
Nilpotent group (3)
Nilpotency class (3)
Isologic groups with respect to fixed nilpotency class lower than theirs have equal nilpotency classNilpotency class (3)
Nilpotent group (3)
Local powering-invariant subgroup containing the center is intermediately local powering-invariant in nilpotent groupNilpotent group (3)
Local powering-invariant subgroup (2)
Intermediately local powering-invariant subgroup (3)
Locally nilpotent not implies nilpotentLocally nilpotent group (2)
Nilpotent group (2)
Lower central series is fastest descending central seriesNilpotent group (?)
Central series (?)
Lower central series (?)
Nilpotency class (?)
Lower central series is strongly centralLower central series (?)
Nilpotent group (?)
Strongly central series (?)
Maximal among abelian characteristic not implies self-centralizing in nilpotentNilpotent group (2)
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)
Minimal normal implies central in nilpotent groupNilpotent group (?)
Minimal normal subgroup (?)
Central subgroup (?)
Minimal normal subgroup of nilpotent group (2)
Central subgroup of nilpotent group (3)
Nilpotency is 2-local for finite groupsNilpotent group (2)
Finite nilpotent group (1)
Nilpotency of fixed class is quotient-closedNilpotent group (1)
Quotient-closed group property (2)
Nilpotency class (1)
Nilpotency of fixed class is subgroup-closedNilpotent group (1)
Subgroup-closed group property (2)
Nilpotency class (1)
Nilpotent Hall implies isomorph-conjugateFinite group (?)
Nilpotent Hall subgroup (?)
Isomorph-conjugate subgroup (?)
Nilpotent Hall subgroup of finite group (2)
Isomorph-conjugate subgroup of finite group (3)
Hall subgroup (?)
Nilpotent group (?)
Nilpotent and every abelian characteristic subgroup is central implies class at most twoNilpotent group (?)
Group in which every abelian characteristic subgroup is central (?)
Nilpotent automorphism group implies nilpotent of class at most one moreGroup whose automorphism group is nilpotent (2)
Nilpotent group (2)
Nilpotent group (?)
Nilpotency class (?)
Nilpotent implies center is normality-largeNilpotent group (3)
Center (2)
Normality-large subgroup (2)
Nilpotent group (2)
Group whose center is normality-large (2)
Nilpotent implies derived in FrattiniNilpotent group (?)
Derived subgroup (?)
Frattini 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 nontrivial normal subgroup contains a cyclic normal subgroupNilpotent group (2)
Group in which every nontrivial normal subgroup contains a cyclic normal subgroup (2)
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)
Nilpotent implies every subgroup is subnormalNilpotent group (2)
Group in which every subgroup is subnormal (2)
Subnormal subgroup (?)
Subnormal depth (?)
Nilpotency class (?)
Nilpotent implies no proper contranormal subgroupNilpotent group (2)
Contranormal subgroup (2)
Nilpotent implies normalizer conditionNilpotent group (?)
Group satisfying normalizer condition (?)
Self-normalizing subgroup (?)
Nilpotent join of intermediately isomorph-conjugate subgroups is intermediately isomorph-conjugateIntermediately isomorph-conjugate subgroup (?)
Nilpotent group (?)
Nilpotent join of pronormal subgroups is pronormalPronormal subgroup (?)
Nilpotent group (?)
Nilpotent not implies ACICNilpotent group (2)
Group in which every automorph-conjugate subgroup is characteristic (2)
Automorph-conjugate subgroup (2)
Characteristic subgroup (2)
Nilpotent not implies UL-equivalentNilpotent group (2)
UL-equivalent group (2)
Upper central series (?)
Lower central series (?)
Nilpotent not implies abelianNilpotent group (2)
Abelian group (2)
Nilpotent not implies generated by abelian normal subgroupsNilpotent group (2)
Group generated by abelian normal subgroups (2)
Nilpotent not implies nilpotent automorphism groupNilpotent group (2)
Group whose automorphism group is nilpotent (2)
Normalizer condition not implies nilpotentGroup satisfying normalizer condition (2)
Nilpotent group (2)
P-group not implies nilpotentP-group (2)
Nilpotent group (2)