Showing 25 pages using this property.
A | |
|---|
| Abelian p-group with indecomposable coprime automorphism group is homocyclic + | Gorenstein (?, ?, ?) + |
| Associative implies generalized associative + | DummitFoote (?, ?, ?) + |
B | |
|---|
| Bryant-Kovacs theorem + | HuppertBlackburnII (?, ?, ?) + |
| Burnside's basis theorem + | DummitFoote (?, ?, ?) + |
| Burnside's theorem on coprime automorphisms and Frattini subgroup + | Gorenstein (?, ?, ?) +, DummitFoote (?, ?, ?) + |
C | |
|---|
| Central product decomposition lemma for characteristic rank one + | Gorenstein (?, ?, ?) + |
| Centralizer product theorem + | Gorenstein (?, ?, ?) + |
| Centralizer product theorem for elementary Abelian group + | Gorenstein (?, ?, ?) + |
| Centralizer-commutator product decomposition + | Gorenstein (?, ?, ?) + |
| Characteristic implies normal + | AlperinBell (?, ?, ?) +, DummitFoote (?, ?, ?) +, Herstein (?, ?, ?) +, … |
| Characteristic of normal implies normal + | DummitFoote (135, Section 4.4 (''Automorphisms''), Point (3) after definition of characteristic subgroup, ?) +, DummitFoote (137, Exercise 8(a), ?) +, RobinsonGT (28, Section 1.5 (''Characteristic and Fully invariant subgroups''), 1.5.6(iii), ?) +, … |
| Characteristically metacyclic and commutator-realizable implies cyclic + | DummitFoote (?, ?, ?) + |
| Characteristicity is transitive + | DummitFoote (137, Problem 8(b), ?) +, AlperinBell (17, Lemma 4, ?) +, RobinsonGT (28, 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''), hints given in exercise) + |
| Classification of extraspecial groups + | Gorenstein (?, ?, ?) + |
| 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 normal self-centralizing subgroup + | Gorenstein (?, ?, ?) + |
| Clifford's theorem + | Gorenstein (?, ?, ?) + |
| Commutator subgroup satisfies ascending chain condition on subnormal subgroups implies subnormal join property + | RobinsonGT (?, ?, ?) + |
| Cube map is automorphism implies Abelian + | Herstein (?, ?, ?) + |
| Cube map is endomorphism iff Abelian (if order is not a multiple of 3) + | Herstein (?, ?, ?) + |
| Cyclic Frattini quotient implies cyclic + | Gorenstein (?, ?, ?) + |
| Cyclic normal implies hereditarily normal + | Herstein (?, ?, ?) + |
