The proof of Orbit Stabliser Theorem. ie.Given a group action on a set X, |Orbit of x|= Index of Stabliser of x in G. This proof is based on John Fraleigh' s Text Section 16.16
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Group Action On a Set Part1
Group Action On a Set Part 2
Group Action On a Set Part 3
Group Action On a Set Part 4
Group Action On a Set Part 5
Stablizer of Group Action on a set.
Fix(g) of Group Action on a set
Orbit of group action
Orbit Stabliser Theorem