Property:Proved in
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| Has typeThis property is a special property in this wiki. | PageThis type is among the standard datatypes of this wiki., NumberThis type is among the standard datatypes of this wiki., StringThis type is among the standard datatypes of this wiki., StringThis type is among the standard datatypes of this wiki. + |
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Pages using the property "Proved in"
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 theorem on coprime automorphisms and Frattini subgroup + | Gorenstein (?, ?, ?) + |
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 + | RobinsonGT (?, ?, ?) +, KhukhroNGA (?, ?, ?) + |
| Characteristic of normal implies normal + | RobinsonGT (28, Section 1.5 (''Characteristic and Fully invariant subgroups''), 1.5.6(iii), ?) + |
| 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 (?, ?, ?) + |
| Cyclic Frattini quotient implies cyclic + | Gorenstein (?, ?, ?) + |
E | |
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| Every nontrivial subgroup of the group of integers is cyclic on its smallest element + | Artin (?, ?, ?) + |
| Extraspecial commutator-in-center subgroup is central factor + | Gorenstein (?, ?, ?) + |
F | |
|---|
| 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 theorem + | Gorenstein (?, ?, ?) + |
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