Property:Referenced in

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Showing 20 pages using this property.
A
Abelian group +
DummitFoote (17, Formal definition (definition as point (2) in general definition of group), Formal definition (definition as point (2) in general definition of group))  +, AlperinBell (2, 1.1 (Rudiments of Group Theory/Review), 1.1 (Rudiments of Group Theory/Review))  +, Artin (42, definition introduced in paragraph (immediately after definition of group), definition introduced in paragraph (immediately after definition of group))  +, …
Associative implies generalized associative +
DummitFoote (?, ?, ?)  +
B
Burnside's basis theorem +
DummitFoote (?, ?, ?)  +
Burnside's theorem on coprime automorphisms and Frattini subgroup +
Gorenstein (?, ?, ?)  +, DummitFoote (?, ?, ?)  +
C
Center +
Herstein (?, ?, ?)  +, AlperinBell (?, ?, ?)  +, DummitFoote (?, ?, ?)  +, …
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)  +, …
Characteristic subgroup +
BurnsideFiniteGroups (92, ?, ?)  +, DummitFoote (135, Section 4.4 (''Automorphisms''), Section 4.4 (''Automorphisms''))  +, Herstein (70, Problem 7(a), Problem 7(a))  +, …
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 +
DummitFoote (?, ?, ?)  +, Hungerford (?, ?, ?)  +, RobinsonGT (?, ?, ?)  +, …
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''))  +, Burnsidep^aq^b (?, ?, ?)  +
Cube map is endomorphism iff abelian (if order is not a multiple of 3) +
Herstein (?, ?, ?)  +
Cyclic group +
DummitFoote (54, formal definition, formal definition)  +, AlperinBell (3, definition introduced in paragraph, definition introduced in paragraph)  +, Herstein (39, Example 2.4.3, Example 2.4.3)  +, …
D
Derived subgroup +
Artin (?, ?, ?)  +, DummitFoote (?, ?, ?)  +, Lang (?, ?, ?)  +, …
Dihedral group +
DummitFoote (?, ?, ?)  +, AlperinBell (?, ?, ?)  +, Lang (?, ?, ?)  +, …
E
Equivalence of definitions of Frattini subgroup +
DummitFoote (?, ?, ?)  +
Equivalence of definitions of Sylow subgroup of normal subgroup +
DummitFoote (?, ?, ?)  +
F
Finite group +
DummitFoote (17, definition given as an additional comment after the formal definition of group, definition given as an additional comment after the formal definition of group)  +, AlperinBell (2, ?, ?)  +, Fraleigh (58, the term is not explicitly defined, but the definition is implicit in the section ''Finite groups and group tables'', the term is not explicitly defined, but the definition is implicit in the section ''Finite groups and group tables'')  +, …
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