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Group
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Mathematics
Area of mathematics
Algebra
OurBigBook.com
words: 3k
articles: 98
Table of contents
3k
98
Center
(group theory)
Group
Group axiom
Group
10
3
Commutative property
Group axiom
10
2
Abelian group
Commutative property
10
1
Non-commutative
Abelian group
Symmetry
Group
8
1
Symmetry breaking
Symmetry
Important mathematical group
Group
301
19
Important discrete mathematical group
Important mathematical group
301
18
Cyclic group
(
C
n
, C sub n)
Important discrete mathematical group
The direct product of two cyclic groups of coprime order is another cyclic group
Important discrete mathematical group
65
Permutation
Important discrete mathematical group
188
11
Cycle notation
Permutation
48
Parity of a permutation
Permutation
2
Odd permutation
Parity of a permutation
Even permutation
Parity of a permutation
Permutation group
Permutation
140
6
Stabilizer
(group)
Permutation group
90
Symmetric group
Permutation group
15
1
All groups are isomorphic to a subgroup of the symmetric group
Symmetric group
12
Alternating group
(
A
n
)
Permutation group
35
2
Alternating group of degree 5
Alternating group
9
1
The alternating groups of degree 5 or greater are simple
Alternating group of degree 5
9
Dihedral group
(
D
n
)
Important discrete mathematical group
34
Wallpaper group
Important discrete mathematical group
3
Space group
Important discrete mathematical group
8
Klein four-group
Important discrete mathematical group
3
Finite group
Group
721
28
Classification of finite groups
Finite group
721
27
List of finite groups
Classification of finite groups
5
1
GroupNames
List of finite groups
5
Classification of finite simple groups
Classification of finite groups
591
23
Group of Lie type
Classification of finite simple groups
156
2
Chevalley group
Group of Lie type
30
1
Chevalley groups
A
n
(
q
)
Chevalley group
30
Sporadic group
Classification of finite simple groups
326
17
Mathieu group
Sporadic group
296
13
k-transitive group
Mathieu group
112
7
Classification of k-transitive groups
k-transitive group
93
6
2-transitive group
Classification of k-transitive groups
1
Classification of 2-transitive groups
2-transitive group
Classification of 3-transitive groups
Classification of k-transitive groups
5
Classification of 4-transitive groups
Classification of k-transitive groups
9
Classification of 5-transitive groups
Classification of k-transitive groups
62
Classification of 6-transitive groups
Classification of k-transitive groups
6
Mathieu group
M
1
1
Mathieu group
Mathieu group
M
1
2
Mathieu group
Mathieu group
M
2
2
Mathieu group
Mathieu group
M
2
3
Mathieu group
Mathieu group
M
2
4
Mathieu group
6
Janko group
Sporadic group
Monster group
Sporadic group
30
1
Monstrous moonshine
Monster group
7
Jordan-Holder Theorem
Classification of finite simple groups
7
Composition series
Classification of finite simple groups
Group extension problem
Classification of finite groups
72
Group operation
Group
Group isomorphism
Group
161
4
Isomorphism
Group isomorphism
73
Group homomorphism
Group isomorphism
88
2
Fundamental theorem on homomorphisms
Group homomorphism
7
Kernel
(algebra)
Group homomorphism
Generating set of a group
Group
240
6
Finitely generated group
Generating set of a group
Rank of a group
Generating set of a group
7
Cayley graph
Generating set of a group
155
1
Cycle graph
(algebra)
Cayley graph
105
Cycle of an element of a group
Generating set of a group
78
1
Order of an element of a group
Cycle of an element of a group
7
Direct product of groups
(
G
×
H
)
Group
318
2
Product of group subsets
Direct product of groups
Semidirect product
(
N
⋊
H
)
Direct product of groups
318
Subgroup
Group
484
7
Subgroup generated by a group
Subgroup
Quotient group
Subgroup
484
5
Subquotient
Quotient group
43
Relationship between the quotient group and direct products
Quotient group
266
Normal subgroup
Quotient group
148
2
Simple group
Normal subgroup
45
1
How to show that a group is simple
Simple group
11
Ring
(mathematics)
Group
996
17
Commutative ring
Ring
13
Division ring
Ring
14
Finite ring
Ring
47
1
Classification of finite rings
Finite ring
47
Field
(mathematics)
Ring
760
12
Multiplicative inverse
Field
Distributive property
Field
28
Finite field
(
G
F
(
n
)
)
Field
615
4
Classification of finite fields
Finite field
64
Finite field of non-prime order
Finite field
85
GF(2)
Finite field
GF(4)
Finite field
302
Quadratically closed field
Field
Vector field
Field
60
3
Algebra over a field
Vector field
55
2
Division algebra
Algebra over a field
14
1
Frobenius theorem
(real division algebras, Classification of associative real division algebras)
Division algebra
11
Ancestors
(4)
Algebra
Area of mathematics
Mathematics
Home
Incoming links
(6)
Algebraic structure
Birch and Swinnerton-Dyer conjecture in two minutes by Ciro Santilli
Cycle graph
Direct product
Invertible matrix
Symmetric group
Synonyms
(1)
Group
Ciro Santilli
OurBigBook.com