| Groups |
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| Basic notions |
- Subgroup
- Normal subgroup
- Quotient group
- Group homomorphism
- (Semi-)direct product
- direct sum
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| Types of groups | * Finite groups
Abelian groups
Cyclic groups
Simple groups
Solvable groups |
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| Discrete groups | ; Classification of finite simple groups
- Cyclic group Zn
- Alternating group An
- Sporadic groups
- Mathieu group M11..12,M22..24
- Conway group Co1..3
- Janko groups J1, J2, J3, J4
- Fischer group F22..24
- Baby Monster group B
- Monster group M
- Other finite groups
- Symmetric group Sn
- Dihedral group Dn
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| 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
- G2
- F4
- E6
- E7
- E8
- Lorentz group
- Poincaré group
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| Infinite dimensional groups | * Conformal group
Diffeomorphism group
Loop group
Quantum group
O(∞)
SU(∞)
Sp(∞) |
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| * History
Applications
Abstract algebra |