Showing 25 pages using this property.
2 | |
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| 2-Sylow subgroup is TI implies it is normal or there is exactly one conjugacy class of involutions + | Book:Gorenstein (302, Chapter 9 (''Groups of even order''), Theorem 1.4, ?) + |
A | |
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| Abelian normal subgroup of core-free maximal subgroup is contranormal implies derived subgroup of whole group is monolith + | Book:Cohn (120, ?, ?) + |
| Abelian p-group with indecomposable coprime automorphism group is homocyclic + | Book:Gorenstein (?, ?, ?) + |
| Alperin's fusion theorem in terms of well-placed tame intersections + | Book:Gorenstein (284, Theorem 4.5, Chapter 8 (''p-constrained and p-stable groups''), Section 4 (''Groups with subgroups of glauberman type''), ?) + |
| Any abelian normal subgroup normalizes an abelian subgroup of maximum order + | Book:Gorenstein (274, Theorem 2.6, Section 8.2 (''Glauberman's theorem''), ?) + |
| Any class two normal subgroup whose derived subgroup is in the ZJ-subgroup normalizes an abelian subgroup of maximum order + | Book:Gorenstein (278, Theorem 2.9, Chapter 8 (''p-constrained and p-stable groups''), Section 2 (''Glauberman's theorem''), ?) + |
| Associative implies generalized associative + | Book:DummitFoote (?, ?, ?) + |
B | |
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| Brauer's induction theorem + | Book:Serre (75, Theorem 18, Section 10.2, ?) + |
| Bryant-Kovacs theorem + | Book:HuppertBlackburnII (403, Theorem 13.5, Chapter 13 (''Automorphisms of p-groups''), ?) + |
| Burnside's basis theorem + | Book:DummitFoote (?, ?, ?) + |
| Burnside's theorem on coprime automorphisms and Frattini subgroup + | Book:Gorenstein (?, ?, ?) +, Book:DummitFoote (?, ?, ?) + |
C | |
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| Central product decomposition lemma for characteristic rank one + | Book:Gorenstein (?, ?, ?) + |
| Centralizer of coprime automorphism in homomorphic image equals image of centralizer + | Book:KhukhroNGA (17, Theorem 1.6.2, ?) + |
| Centralizer product theorem + | Book:Gorenstein (188, Theorem 3.16, Chapter 5, Section 3 (''p'-automorphisms of p-groups''), ?) + |
| Centralizer product theorem for elementary abelian group + | Book:Gorenstein (69, Theorem 3.3, Chapter 3, Section 3 (''Complete reducibility''), ?) + |
| Centralizer-commutator product decomposition for finite groups and cyclic automorphism group + | Book:KhukhroNGA (18, Corollary 1.6.4, Proof uses theorem 1.6.2) + |
| Centralizer-commutator product decomposition for finite nilpotent groups + | Book:Gorenstein (180, Theorem 3.5, Section 5.3 (''p'-automorphisms of p-groups''), proved only for groups of prime power order, but the same proof technique) + |
| 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 + | Book:Gorenstein (255, Theorem 5.1, Chapter 7 (''Fusion, transfer and p-factor groups''), Section 7.5 (''Weak closure and p-normality''), ?) + |
| Characteristically metacyclic and commutator-realizable implies abelian + | Book:DummitFoote (?, ?, ?) + |
| 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 + | Book:DummitFoote (149, Exercises 54-55, Section 4.5 (''Sylow's theorem''), hints given in exercise) + |
| Classification of extraspecial groups + | Book:Gorenstein (?, ?, ?) + |
| Classification of finite 2-groups of maximal class + | Book:Gorenstein (194, Section 5.4 (''p-groups of small depth''), Theorem 4.5, ?) + |
