Showing 25 pages using this property.
2 | |
|---|
| 2-Sylow subgroup is TI implies it is normal or there is exactly one conjugacy class of involutions + | ? (?, ?, ?) + |
A | |
|---|
| Abelian normal subgroup of core-free maximal subgroup is contranormal implies derived subgroup of whole group is monolith + | ? (?, ?, ?) + |
| Abelian p-group with indecomposable coprime automorphism group is homocyclic + | ? (?, ?, ?) + |
| Alperin's fusion theorem in terms of well-placed tame intersections + | ? (?, ?, ?) + |
| Any abelian normal subgroup normalizes an abelian subgroup of maximum order + | ? (?, ?, ?) + |
| Any class two normal subgroup whose derived subgroup is in the ZJ-subgroup normalizes an abelian subgroup of maximum order + | ? (?, ?, ?) + |
| Associative implies generalized associative + | ? (?, ?, ?) + |
B | |
|---|
| Brauer's induction theorem + | Book:Serre (75, Theorem 18, Section 10.2, ?) + |
| Bryant-Kovacs theorem + | ? (?, ?, ?) + |
| Burnside's basis theorem + | Book:DummitFoote (?, ?, ?) + |
| Burnside's theorem on coprime automorphisms and Frattini subgroup + | ? (?, ?, ?) +, ? (?, ?, ?) + |
C | |
|---|
| Central product decomposition lemma for characteristic rank one + | ? (?, ?, ?) + |
| Centralizer of coprime automorphism in homomorphic image equals image of centralizer + | ? (?, ?, ?) + |
| Centralizer product theorem + | ? (?, ?, ?) + |
| Centralizer product theorem for elementary abelian group + | ? (?, ?, ?) + |
| Centralizer-commutator product decomposition for finite groups and cyclic automorphism group + | ? (?, ?, ?) + |
| Centralizer-commutator product decomposition for finite nilpotent groups + | ? (?, ?, ?) + |
| Characteristic implies normal + | Book:AlperinBell (?, ?, ?) +, Book:DummitFoote (?, ?, ?) +, Book:Herstein (?, ?, ?) +, … |
| Characteristic of normal implies normal + | Book:DummitFoote (135, Section 4.4 (''Automorphisms''), Point (3) after definition of characteristic subgroup, ?) +, DummitFoote (137, Exercise 8(a), ?) +, Book:RobinsonGT (28, 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 + | ? (?, ?, ?) + |
| Characteristically metacyclic and commutator-realizable implies abelian + | ? (?, ?, ?) + |
| Characteristicity is transitive + | Book:DummitFoote (137, Problem 8(b), ?) +, Book:AlperinBell (17, Lemma 4, ?) +, Book:RobinsonGT (28, Section 1.5 (''Characteristic and Fully invariant subgroups''), 1.5.6(ii), ?) +, … |
| Classification of cyclicity-forcing numbers + | ? (?, ?, ?) + |
| Classification of extraspecial groups + | ? (?, ?, ?) + |
| Classification of finite 2-groups of maximal class + | ? (?, ?, ?) + |
