Abelian implies nilpotent | | Abelian group (2) Nilpotent group (2) |

Ambivalent and nilpotent implies 2-group | | Ambivalent group (2) Nilpotent group (3) |

C-closed implies completely divisibility-closed in nilpotent group | | Nilpotent 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 nilpotent | | CA-group (2) Nilpotent group (2) CN-group (2) Abelian group (3) |

Commutator-verbal implies divisibility-closed in nilpotent group | | Nilpotent 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 nilpotent | | Commuting fraction (2) Nilpotent group (3) Finite nilpotent group (3) Number of conjugacy classes (3) |

Comparable with all normal subgroups implies normal in nilpotent group | | Nilpotent 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 class | | Nilpotent group (?) Derived length (?) Nilpotency class (?) |

Derived length is logarithmically bounded by nilpotency class | | Nilpotent group (3) Nilpotency class (2) Solvable group (3) Derived length (2) |

Derived subgroup not is intermediately powering-invariant in nilpotent group | | Nilpotent group (3) Derived subgroup (2) Intermediately powering-invariant subgroup (2) |

Divisibility-closedness is strongly join-closed in nilpotent group | | Nilpotent group (?) Divisibility-closed subgroup (?) Strongly join-closed subgroup property (?) |

Epicentral series members are completely divisibility-closed in nilpotent group | | Nilpotent group (3) Epicentral series (3) Completely divisibility-closed subgroup (3) Epicenter (3) |

Equivalence of definitions of nilpotent group | | Nilpotent group (1) |

Equivalence of definitions of periodic nilpotent group | | Periodic 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 simple | | Nilpotent group (3) Finite nilpotent group (3) |

Group with nilpotent derived subgroup | | Derived subgroup (?) Nilpotent group (?) Nilpotent normal subgroup (?) Nilpotent characteristic subgroup (?) |

Intermediately automorph-conjugate implies intermediately characteristic in nilpotent | | Nilpotent 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 nilpotent | | Nilpotent 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 class | | Isoclinic groups (?) Nilpotent group (3) Nilpotency class (3) |

Isologic groups with respect to fixed nilpotency class lower than theirs have equal nilpotency class | | Nilpotency class (3) Nilpotent group (3) |

Local powering-invariant subgroup containing the center is intermediately local powering-invariant in nilpotent group | | Nilpotent group (3) Local powering-invariant subgroup (2) Intermediately local powering-invariant subgroup (3) |

Locally nilpotent not implies nilpotent | | Locally nilpotent group (2) Nilpotent group (2) |

Lower central series is fastest descending central series | | Nilpotent group (?) Central series (?) Lower central series (?) Nilpotency class (?) |

Lower central series is strongly central | | Lower central series (?) Nilpotent group (?) Strongly central series (?) |

Maximal among abelian characteristic not implies self-centralizing in nilpotent | | Nilpotent group (2) |

Maximal among abelian normal implies self-centralizing in nilpotent | | Nilpotent 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 group | | Nilpotent 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 groups | | Nilpotent group (2) Finite nilpotent group (1) |

Nilpotency of fixed class is quotient-closed | | Nilpotent group (1) Quotient-closed group property (2) Nilpotency class (1) |

Nilpotency of fixed class is subgroup-closed | | Nilpotent group (1) Subgroup-closed group property (2) Nilpotency class (1) |

Nilpotent Hall implies isomorph-conjugate | | Finite 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 two | | Nilpotent group (?) Group in which every abelian characteristic subgroup is central (?) |

Nilpotent automorphism group implies nilpotent of class at most one more | | Group whose automorphism group is nilpotent (2) Nilpotent group (2) Nilpotent group (?) Nilpotency class (?) |

Nilpotent implies center is normality-large | | Nilpotent group (3) Center (2) Normality-large subgroup (2) Nilpotent group (2) Group whose center is normality-large (2) |

Nilpotent implies derived in Frattini | | Nilpotent group (?) Derived subgroup (?) Frattini subgroup (?) |

Nilpotent implies every maximal subgroup is normal | | Nilpotent 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 subgroup | | Nilpotent group (2) Group in which every nontrivial normal subgroup contains a cyclic normal subgroup (2) |

Nilpotent implies every normal subgroup is potentially characteristic | | Nilpotent group (?) Normal subgroup (?) Potentially characteristic subgroup (?) Normal subgroup of nilpotent group (2) Potentially characteristic subgroup of nilpotent group (3) |

Nilpotent implies every subgroup is subnormal | | Nilpotent group (2) Group in which every subgroup is subnormal (2) Subnormal subgroup (?) Subnormal depth (?) Nilpotency class (?) |

Nilpotent implies no proper contranormal subgroup | | Nilpotent group (2) Contranormal subgroup (2) |

Nilpotent implies normalizer condition | | Nilpotent group (?) Group satisfying normalizer condition (?) Self-normalizing subgroup (?) |

Nilpotent join of intermediately isomorph-conjugate subgroups is intermediately isomorph-conjugate | | Intermediately isomorph-conjugate subgroup (?) Nilpotent group (?) |

Nilpotent join of pronormal subgroups is pronormal | | Pronormal subgroup (?) Nilpotent group (?) |

Nilpotent not implies ACIC | | Nilpotent group (2) Group in which every automorph-conjugate subgroup is characteristic (2) Automorph-conjugate subgroup (2) Characteristic subgroup (2) |

Nilpotent not implies UL-equivalent | | Nilpotent group (2) UL-equivalent group (2) Upper central series (?) Lower central series (?) |

Nilpotent not implies abelian | | Nilpotent group (2) Abelian group (2) |

Nilpotent not implies generated by abelian normal subgroups | | Nilpotent group (2) Group generated by abelian normal subgroups (2) |

Nilpotent not implies nilpotent automorphism group | | Nilpotent group (2) Group whose automorphism group is nilpotent (2) |

Normalizer condition not implies nilpotent | | Group satisfying normalizer condition (2) Nilpotent group (2) |

P-group not implies nilpotent | | P-group (2) Nilpotent group (2) |