1
Group G
Set X
x ∈ X
Orb( x ) = { σ. x ∈ X | σ∈G }
x’s stabilizer Gx
Gx = { σ∈ G | σ. x = x }
X’s orbit space on operation G G \ X
2
x ∈ X
Mapping f : G → Orb ( x ) f ( σ) = σ. x σ∈ G
ξ ∈ Gx
ξ.x = x
f ( σGx ) → f (σ) σ∈G
f : G / Gx → Orb ( x )
G’s orbit on operation X is unique.
[Note]
Orbit may be helpful to quantum’s movement on Quantum Theory for Language.
[References]
Tokyo July 24, 2007
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