146
U

# Property:Proved in

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## Pages using the property "Proved in"

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C
Corollary of Thompson transitivity theorem +Gorenstein (293, Theorem 5.6, Chapter 8, Theorem 5.6, Chapter 8)  +
Corollary of centralizer product theorem for rank at least three +Gorenstein (292, Lemma 5.5, Chapter 8 (''p-constrained and p-stable groups''), Section 5 (''The Thompson Transitivity Theorem''), Lemma 5.5, Chapter 8 (''p-constrained and p-stable groups''), Section 5 (''The Thompson Transitivity Theorem''))  +
Criterion for projective representation to lift to linear representation +IsaacsCT (182, Theorem 11.13, Theorem 11.13)  +
Cyclic Frattini quotient implies cyclic +Gorenstein (?, ?, ?)  +
D
Derived subgroup satisfies ascending chain condition on subnormal subgroups implies subnormal join property +RobinsonGT (?, ?, ?)  +
Dickson's theorem +Gorenstein (44, Theorem 8.4, Chapter 2 (''Some basic topics''), Section 2.8 (''Two-dimensional linear and projective groups''), Theorem 8.4, Chapter 2 (''Some basic topics''), Section 2.8 (''Two-dimensional linear and projective groups''))  +
Dihedral trick +Gorenstein (301, Theorem 1.1, Chapter 9 (''Groups of even order''), Section 1 (''Elementary properties of involutions''), Theorem 1.1, Chapter 9 (''Groups of even order''), Section 1 (''Elementary properties of involutions''))  +
E
Every Sylow subgroup is cyclic implies metacyclic +Hall (146, Theorem 9.4.3, Theorem 9.4.3)  +, Gorenstein (258, Theorem 6.2, Chapter 7 (''Fusion, transfer and p-factor groups''), Section 7.6 (''elementary applications''), Theorem 6.2, Chapter 7 (''Fusion, transfer and p-factor groups''), Section 7.6 (''elementary applications''))  +
Every nontrivial subgroup of the group of integers is cyclic on its smallest element +Artin (?, ?, ?)  +
Exactly n elements of order dividing n in a finite solvable group implies the elements form a subgroup +Hall (145, Theorem 9.4.1, Theorem 9.4.1)  +
Extraspecial commutator-in-center subgroup is central factor +Gorenstein (?, ?, ?)  +
F
Finite group having at least two conjugacy classes of involutions has order less than the cube of the maximum of orders of centralizers of involutions +Gorenstein (301, Chapter 9 (''Groups of even order''), Theorem 1.3, Chapter 9 (''Groups of even order''), Theorem 1.3)  +
Finite non-abelian 2-group has maximal class iff its abelianization has order four +Gorenstein (194, Section 5.4 (''p-groups of small depth''), Theorem 4.5, Section 5.4 (''p-groups of small depth''), Theorem 4.5)  +
First isomorphism theorem +Artin (?, ?, ?)  +, DummitFoote (?, ?, ?)  +
Fixed-point-free automorphism of order four implies solvable +Gorenstein (?, ?, ?)  +
Fixed-point-free automorphism of order three implies nilpotent +Gorenstein (?, ?, ?)  +
Fixed-point-free involution on finite group is inverse map +Gorenstein (?, ?, ?)  +
Focal subgroup of a Sylow subgroup is generated by the commutators with normalizers of non-identity tame intersections +Gorenstein (251, Theorem 4.1, Chapter 7 (''Fusion, Transfer and p-factor groups''), Section 7.4 (''Theorems of Burnside, Frobenius, and Grün''), Theorem 4.1, Chapter 7 (''Fusion, Transfer and p-factor groups''), Section 7.4 (''Theorems of Burnside, Frobenius, and Grün''))  +
Focal subgroup theorem +Gorenstein (?, ?, ?)  +
Frattini-in-center odd-order p-group implies p-power map is endomorphism +Gorenstein (?, ?, ?)  +