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Words: 3k
Articles: 113
Group theory studies groups, homomorphisms, actions, quotients, and symmetry.
Table of contents
3k
113
Group
Group theory
296
15
Finite group
Group
28
1
Order of a finite group
Finite group
12
Nontrivial group
Group
8
Identity element
Group
13
Inverse element
Group
11
Group operation
Group
21
Translation in a group
Group
16
Cyclic group
Group
77
2
Finite subgroup of the multiplicative complex numbers
Cyclic group
28
Generator of a group
Cyclic group
22
Abelian group
Group
16
Finite additive group
Group
31
Subgroup
Group
57
2
Index of a subgroup
Subgroup
14
Index-two subgroup is normal
Subgroup
27
First isomorphism theorem
Group theory
14
Direct product of groups
Group theory
19
Commutator subgroup
Group theory
47
1
Abelianization
Commutator subgroup
21
Center of a group
Group theory
28
1
Cyclic quotient by the center
Center of a group
28
Conjugate subgroup
Group theory
Group action
Group theory
250
11
Conjugation action
Group action
27
1
Normalizer
Conjugation action
10
Orbit-stabilizer theorem
Group action
31
Doubly transitive group action
Group action
26
Symmetry group of a cube
Group action
43
Faithful group action
Group action
70
1
Normal subgroup orbits in a faithful prime-degree action
Faithful group action
54
Orbit of a group action
Group action
8
Stabilizer subgroup
Group action
9
Symmetric group action on subsets
Group action
15
Coset action
Group action
21
Coset
Group theory
111
2
Double coset
Coset
87
1
Sylow subgroup of a subgroup from double cosets
Double coset
48
Lagrange's theorem
Group theory
30
Group embedding
Group theory
94
2
Cayley theorem
Group embedding
75
1
Symmetric-group embedding at one less than the group order
Cayley theorem
56
Generalized dihedral group
Group theory
28
Order of a group element
Group theory
Quotient group
Group theory
General linear group
Group theory
21
Special linear group
Group theory
Group homomorphism
Group theory
55
3
Homomorphism between cyclic groups
Group homomorphism
22
Kernel of a group homomorphism
Group homomorphism
10
Image of a group homomorphism
Group homomorphism
16
Automorphism group
Group theory
16
Finite group theory
Group theory
883
33
Alternating group
Finite group theory
P-group
Finite group theory
Symmetric group
Finite group theory
155
6
Sign homomorphism
Symmetric group
37
Permutation cycle
Symmetric group
63
2
Three-cycle
Permutation cycle
23
Disjoint permutation cycles
Permutation cycle
16
Support of a permutation
Symmetric group
24
Sign of a permutation
Symmetric group
31
Quaternion group
Finite group theory
12
Dicyclic group
Finite group theory
25
Simple group
Finite group theory
70
2
Simplicity of the alternating group A5
Simple group
38
Smallest nonabelian simple group
Simple group
17
General linear group over a finite field
Finite group theory
147
6
Order of a general linear group over a finite field
General linear group over a finite field
10
Upper unitriangular group
General linear group over a finite field
30
Projective general linear group action on the projective line
General linear group over a finite field
79
2
Projective line
Projective general linear group action on the projective line
22
Sylow 2-subgroup of PGL2 over F4
Projective general linear group action on the projective line
37
Special linear group over a finite field
General linear group over a finite field
10
Dihedral group
Finite group theory
25
Sylow theorems
Finite group theory
351
7
Sylow subgroup
Sylow theorems
17
Nonabelian group of order pq
Sylow theorems
34
Conjugation action on Sylow subgroups
Sylow theorems
17
Sylow subgroups of S3, S4 and A5
Sylow theorems
63
Sylow containment from a coset fixed point
Sylow theorems
42
Sylow counts in a faithful degree-seven action with S4 point stabilizers
Sylow theorems
75
Even-involution coset fixed-point lemma
Sylow theorems
67
Cauchy theorem for groups
Finite group theory
61
Composition series
Finite group theory
13
Klein four-group
Finite group theory
15
Torsion element
Group theory
6
Free abelian group
Group theory
23
Normal subgroup
Group theory
37
2
Preimage of a normal subgroup
Normal subgroup
12
Image of a normal subgroup
Normal subgroup
12
Dedekind group
Group theory
12
Projective linear group
Group theory
315
11
Möbius transformation
Projective linear group
286
9
Cross-ratio
Möbius transformation
25
Generalized circle under a Möbius transformation
Möbius transformation
43
Affine subgroup of the Möbius group
Möbius transformation
32
Fixed point of a Möbius transformation
Möbius transformation
81
2
Prescribed fixed points of a Möbius transformation
Fixed point of a Möbius transformation
34
Fixed points of a finite-order Möbius transformation
Fixed point of a Möbius transformation
32
Constant-argument locus of a Möbius transformation
Möbius transformation
27
Classification of Möbius transformations by trace
Möbius transformation
18
Möbius maps commuting with reflection in the unit circle
Möbius transformation
34
Matrix representative of a Möbius transformation
Projective linear group
18
Semidirect product
Group theory
141
4
Affine group over a finite field
Semidirect product
126
3
Affine Galois group of the splitting field of x to the p minus two
Affine group over a finite field
40
Affine semidirect product of cyclic groups of orders eleven and five
Affine group over a finite field
71
1
Conjugacy classes in the affine semidirect product of orders eleven and five
Affine semidirect product of cyclic groups of orders eleven and five
38
Solvable group
Group theory
12
Exponent of a finite group
Group theory
60
1
Finite subgroup of a field multiplicative group is cyclic
Exponent of a finite group
42
Order of an element of a finite group
Group theory
22
Ancestors
(4)
Algebra
Area of mathematics
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