146
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2
2-Sylow subgroup is TI implies it is normal or there is exactly one conjugacy class of involutions +Gorenstein (302, Chapter 9 (''Groups of even order''), Theorem 1.4, Chapter 9 (''Groups of even order''), Theorem 1.4)  +
3
3-step group implies solvable CN-group +Gorenstein (401, Lemma 14.1.4, Lemma 14.1.4)  +
A
Abelian normal subgroup of core-free maximal subgroup is contranormal implies derived subgroup of whole group is monolith +Cohn (120, ?, ?)  +
Abelian p-group with indecomposable coprime automorphism group is homocyclic +Gorenstein (?, ?, ?)  +
Alperin's fusion theorem in terms of well-placed tame intersections +Gorenstein (284, Theorem 4.5, Chapter 8 (''p-constrained and p-stable groups''), Section 4 (''Groups with subgroups of glauberman type''), Theorem 4.5, Chapter 8 (''p-constrained and p-stable groups''), Section 4 (''Groups with subgroups of glauberman type''))  +
Analogue of Thompson transitivity theorem fails for abelian subgroups of rank two +Gorenstein (299, Exercise 8, end of Chapter 8, Exercise 8, end of Chapter 8)  +
Analogue of Thompson transitivity theorem fails for groups in which not every p-local subgroup is p-constrained +Gorenstein (299, Exercise 7, Chapter 8, Exercise 7, Chapter 8)  +
Any abelian normal subgroup normalizes an abelian subgroup of maximum order +Gorenstein (274, Theorem 2.6, Section 8.2 (''Glauberman's theorem''), 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 +Gorenstein (278, Theorem 2.9, Chapter 8 (''p-constrained and p-stable groups''), Section 2 (''Glauberman's theorem''), Theorem 2.9, Chapter 8 (''p-constrained and p-stable groups''), Section 2 (''Glauberman's theorem''))  +
Associative implies generalized associative +DummitFoote (?, ?, ?)  +
B
Brauer's induction theorem +Serre (75, Theorem 18, Section 10.2, Theorem 18, Section 10.2)  +
Brauer-Fowler inequality relating number of conjugacy classes of strongly real elements and number of involutions +Gorenstein (306, Chapter 9 (''Groups of even order''), Theorem 1.8, Chapter 9 (''Groups of even order''), Theorem 1.8)  +
Brauer-Fowler theorem on existence of subgroup of order greater than the cube root of the group order +Gorenstein (303, Chapter 9 (''Groups of even order''), Theorem 1.6, Chapter 9 (''Groups of even order''), Theorem 1.6)  +
Bryant-Kovacs theorem +HuppertBlackburnII (403, Theorem 13.5, Chapter 13 (''Automorphisms of p-groups''), Theorem 13.5, Chapter 13 (''Automorphisms of p-groups''))  +
Burnside's theorem on coprime automorphisms and Frattini subgroup +Gorenstein (?, ?, ?)  +
C
Central product decomposition lemma for characteristic rank one +Gorenstein (?, ?, ?)  +
Centralizer of coprime automorphism in homomorphic image equals image of centralizer +KhukhroNGA (17, Theorem 1.6.2, Theorem 1.6.2)  +
Centralizer product theorem +Gorenstein (188, Theorem 3.16, Chapter 5, Section 3 (''p'-automorphisms of p-groups''), Theorem 3.16, Chapter 5, Section 3 (''p'-automorphisms of p-groups''))  +
Centralizer product theorem for elementary abelian group +Gorenstein (69, Theorem 3.3, Chapter 3, Section 3 (''Complete reducibility''), Theorem 3.3, Chapter 3, Section 3 (''Complete reducibility''))  +
Centralizer-commutator product decomposition for finite groups and cyclic automorphism group +KhukhroNGA (18, Corollary 1.6.4, Corollary 1.6.4)  +