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Property:Proved in

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This property is a special property in this wiki.

Pages using the property "Proved in"

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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)  +