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Groups
Basic notions
Subgroup
Normal subgroup
Commutator subgroup
Quotient group
Group homomorphism
(
Semi-
)
direct product
direct sum
Types of groups
Finite groups
Abelian groups
Cyclic groups
Infinite group
Simple groups
Solvable groups
Symmetry group
Space group
Point group
Wallpaper group
Trivial group
Discrete groups
Classification of finite simple groups
Cyclic group
Z
n
Alternating group
A
n
Sporadic groups
Mathieu group
M
11..12
,M
22..24
Conway group
Co
1..3
Janko groups
J
1
,
J
2
,
J
3
,
J
4
Fischer group
F
22..24
Baby monster group
B
Monster group
M
Other finite groups
Symmetric group
S
n
Dihedral group
D
n
Rubik's Cube group
Lie groups
General linear group
GL(n)
Special linear group
SL(n)
Orthogonal group
O(n)
Special orthogonal group
SO(n)
Unitary group
U(n)
Special unitary group
SU(n)
Symplectic group
Sp(n)
Exceptional Lie groups
G
2
F
4
E
6
E
7
E
8
Circle group
Lorentz group
Poincaré group
Quaternion group
Infinite dimensional groups
Conformal group
Diffeomorphism group
Loop group
Quantum group
O(∞)
SU(∞)
Sp(∞)
History
Applications
Abstract algebra
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