Property:Proved in

From Groupprops

record PageThis property is a special property in this wiki., Number"Number" is a type and predefined property provided by Semantic MediaWiki to represent numeric values., TextThis property is a special property in this wiki., TextThis property is a special property in this wiki.

previous 202050100250500next 20
Showing 20 pages using this property.
A
Associative implies generalized associative +
DummitFoote (?, ?, ?)  +
B
Burnside's theorem on coprime automorphisms and Frattini subgroup +
Gorenstein (?, ?, ?)  +
C
Characteristic implies normal +
RobinsonGT (?, ?, ?)  +, KhukhroNGA (?, ?, ?)  +
Characteristic of normal implies normal +
RobinsonGT (28, Section 1.5 (''Characteristic and Fully invariant subgroups''), 1.5.6(iii), Section 1.5 (''Characteristic and Fully invariant subgroups''), 1.5.6(iii))  +
Conjugacy class of prime power size implies not simple +
DummitFoote (890, Lemma 7, Section 19.2 (''Theorems of Burnside and Hall''), Lemma 7, Section 19.2 (''Theorems of Burnside and Hall''))  +
F
First isomorphism theorem +
Artin (?, ?, ?)  +, DummitFoote (?, ?, ?)  +
Fixed-point-free involution on finite group is inverse map +
Gorenstein (?, ?, ?)  +
G
Glauberman's theorem on intersection with the ZJ-subgroup +
Gorenstein (278, Theorem 2.10, Chapter 8 (''p-constrained and p-stable groups''), Section 8.2 (''Glauberman's theorem''), Theorem 2.10, Chapter 8 (''p-constrained and p-stable groups''), Section 8.2 (''Glauberman's theorem''))  +
H
Hall subgroups exist in finite solvable group +
DummitFoote (?, ?, ?)  +
I
Intersection of subgroups is subgroup +
DummitFoote (62, Section 2.4 (''Subgroups generated by subsets of a group''), Proposition 8, Section 2.4 (''Subgroups generated by subsets of a group''), Proposition 8)  +, RobinsonGT (8, Section 1.3 (''Intersections and joins of subgroups''), Proposition 1.3.2, Section 1.3 (''Intersections and joins of subgroups''), Proposition 1.3.2)  +, RobinsonGT (48, 3.3.4, 3.3.4)  +
Inverse map is involutive +
DummitFoote (?, ?, ?)  +
L
Lagrange's theorem +
Artin (?, ?, ?)  +, DummitFoote (?, ?, ?)  +
Left and right coset spaces are naturally isomorphic +
AlperinBell (?, ?, ?)  +
Left cosets partition a group +
DummitFoote (?, ?, ?)  +
M
Maximal subgroup has prime power index in finite solvable group +
Gorenstein (?, ?, ?)  +
N
Normal subgroup equals kernel of homomorphism +
DummitFoote (?, ?, ?)  +
Normality is not transitive +
AlperinBell (8, ?, ?)  +, DummitFoote (91, Section 3.2 (''More on cosets and Lagrange's theorem''), Example (3), Section 3.2 (''More on cosets and Lagrange's theorem''), Example (3))  +
O
Order has only two prime factors implies solvable +
DummitFoote (886, Section 19.2 (''Theorems of Burnside and Hall''), Section 19.2 (''Theorems of Burnside and Hall''))  +
P
P-constrained and p-stable implies abelian normal subgroup of Sylow subgroup is contained in (p',p)-core +
Gorenstein (270, Theorem 1.3, Chapter 8 (''p-constrained and p-stable groups''), Theorem 1.3, Chapter 8 (''p-constrained and p-stable groups''))  +
S
Second isomorphism theorem +
DummitFoote (97, Theorem 18 of Section 3.3, Theorem 18 of Section 3.3)  +
Retrieved from "https://groupprops.subwiki.org/w/index.php?title=Property:Proved_in&oldid=25084"