Math 412. The Orbit Stabilizer Theorem
By-NC-SA 4.0 International License. Math 412. The Orbit Stabilizer Theorem Fix an action of a group G on a set X. For each point x of X, we have two important concepts: DEFINITION: The orbit of x 2X is the subset of X O(x) := fg xjg 2GgˆX: DEFINITION: The stabilizer of x is the subgroup of G Stab(x) = fg 2G jg x = xgˆG:
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