Property:Stated in

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Showing 20 pages using this property.
A
Associative implies generalized associative +
DummitFoote (?, ?, ?)  +
B
Burnside's basis theorem +
DummitFoote (?, ?, ?)  +
Burnside's theorem on coprime automorphisms and Frattini subgroup +
Gorenstein (?, ?, ?)  +, DummitFoote (?, ?, ?)  +
C
Characteristic implies normal +
RobinsonGT (?, ?, ?)  +, KhukhroNGA (?, ?, ?)  +, AlperinBell (?, ?, ?)  +, …
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))  +, DummitFoote (135, Section 4.4 (''Automorphisms''), Point (3) after definition of characteristic subgroup, Section 4.4 (''Automorphisms''), Point (3) after definition of characteristic subgroup)  +, Herstein (70, Problem 9, Problem 9)  +, …
Characteristically metacyclic and commutator-realizable implies abelian +
DummitFoote (?, ?, ?)  +
Characteristicity is transitive +
DummitFoote (137, Problem 8(b), Problem 8(b))  +, AlperinBell (17, Lemma 4, Lemma 4)  +, RobinsonGT (28, Section 1.5 (''Characteristic and Fully invariant subgroups''), 1.5.6(ii), Section 1.5 (''Characteristic and Fully invariant subgroups''), 1.5.6(ii))  +, …
Classification of cyclicity-forcing numbers +
DummitFoote (149, Exercises 54-55, Section 4.5 (''Sylow's theorem''), Exercises 54-55, Section 4.5 (''Sylow's theorem''))  +
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''))  +
Cube map is endomorphism iff abelian (if order is not a multiple of 3) +
Herstein (?, ?, ?)  +
E
Equivalence of definitions of Frattini subgroup +
DummitFoote (?, ?, ?)  +
Equivalence of definitions of Sylow subgroup of normal subgroup +
DummitFoote (?, ?, ?)  +
F
Finite non-abelian and every proper subgroup is abelian implies metabelian +
DummitFoote (149, Exercise 56 of Section 4.5 (''Sylow's theorem''), Exercise 56 of Section 4.5 (''Sylow's theorem''))  +
Finite non-abelian and every proper subgroup is abelian implies not simple +
DummitFoote (149, Exercise 53 of Section 4.5 (''Sylow's theorem''), Exercise 53 of Section 4.5 (''Sylow's theorem''))  +
First isomorphism theorem +
Artin (?, ?, ?)  +, DummitFoote (?, ?, ?)  +
Fixed-point-free involution on finite group is inverse map +
Gorenstein (?, ?, ?)  +, Herstein (?, ?, ?)  +, DummitFoote (?, ?, ?)  +
Fourth isomorphism theorem +
DummitFoote (?, ?, ?)  +, Artin (?, ?, ?)  +
Frattini subgroup is nilpotent in finite +
DummitFoote (?, ?, ?)  +
Frattini subgroup is normal-monotone +
DummitFoote (?, ?, ?)  +
G
Glauberman's theorem on intersection with the ZJ-subgroup +
Gorenstein (278, Theorem 2.10, Chapter 8 (''p-constrained and p-stable groups''), Section 8.2 (''Glauberman's theorem''), Theorem 2.10, Chapter 8 (''p-constrained and p-stable groups''), Section 8.2 (''Glauberman's theorem''))  +
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