Orbit of Group Action

up:: Group Action

Given a Group Action of a Group upon a set , we have that the orbit of a point is the set of all points in the set which are reached from after being acted upon by . That is,

Note that Group actions induce an equivalence relation over a set’s orbits, since distinct orbits are disjoint and cover the entire set .

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References

• abstract algebra - Intuitive definitions of the Orbit and the Stabilizer - Mathematics Stack Exchange