Centralizer-commutator product decomposition for finite nilpotent groups + | Gorenstein (180, Theorem 3.5, Section 5.3 (''p'-automorphisms of p-groups''), Theorem 3.5, Section 5.3 (''p'-automorphisms of p-groups'')) + |

Characteristic implies normal + | RobinsonGT (?, ?, ?) +, KhukhroNGA (?, ?, ?) + |

Characteristic of normal implies normal + | RobinsonGT (28, Section 1.5 (''Characteristic and Fully invariant subgroups''), 1.5.6(iii), Section 1.5 (''Characteristic and Fully invariant subgroups''), 1.5.6(iii)) + |

Characteristic subgroup of Sylow subgroup is weakly closed iff it is normal in every Sylow subgroup containing it + | Gorenstein (255, Theorem 5.1, Chapter 7 (''Fusion, transfer and p-factor groups''), Section 7.5 (''Weak closure and p-normality''), Theorem 5.1, Chapter 7 (''Fusion, transfer and p-factor groups''), Section 7.5 (''Weak closure and p-normality'')) + |

Classification of extraspecial groups + | Gorenstein (?, ?, ?) + |

Classification of finite 2-groups of maximal class + | Gorenstein (194, Section 5.4 (''p-groups of small depth''), Theorem 4.5, Section 5.4 (''p-groups of small depth''), Theorem 4.5) + |

Classification of finite p-groups of characteristic rank one + | Gorenstein (?, ?, ?) + |

Classification of finite p-groups of normal rank one + | Gorenstein (?, ?, ?) + |

Classification of finite p-groups of rank one + | Gorenstein (?, ?, ?) + |

Classification of finite p-groups with cyclic maximal subgroup + | Gorenstein (193, Section 5.4 (''pgroups of small depth''), Theorem 4.4, Section 5.4 (''pgroups of small depth''), Theorem 4.4) + |

Classification of finite p-groups with cyclic normal self-centralizing subgroup + | Gorenstein (?, ?, ?) + |

Classification of finite solvable CN-groups + | Gorenstein (402, Theorem 14.1.5, Theorem 14.1.5) + |

Clifford's theorem + | Gorenstein (?, ?, ?) + |

Commutator of finite group with cyclic coprime automorphism group equals second commutator + | KhukhroNGA (18, Corollary 1.6.4(b), Corollary 1.6.4(b)) + |

Commutator of finite nilpotent group with coprime automorphism group equals second commutator + | Gorenstein (181, Theorem 3.6, Section 5.3 (''p'-automorphisms of p-groups''), Theorem 3.6, Section 5.3 (''p'-automorphisms of p-groups'')) + |

Commuting of non-identity elements defines an equivalence relation between prime divisors of the order of a finite CN-group + | Gorenstein (408, Theorem 14.2.5(i), Theorem 14.2.5(i)) + |

Conjugacy class of prime power size implies not simple + | DummitFoote (890, Lemma 7, Section 19.2 (''Theorems of Burnside and Hall''), Lemma 7, Section 19.2 (''Theorems of Burnside and Hall'')) + |

Conjugacy functor whose normalizer generates whole group with p'-core controls fusion + | Gorenstein (282, Theorem 4.1, Theorem 4.1) + |

Core-free and permutable implies subdirect product of finite nilpotent groups + | LennoxStonehewer (217, Theorem 7.1.10(a), Theorem 7.1.10(a)) + |

Core-free permutable subnormal implies solvable of length at most one less than subnormal depth + | LennoxStonehewer (214, Theorem 7.1.5, Theorem 7.1.5) + |