Studying the Proof of the Orbit-Stabilizer Theorem

The Orbit-Stabilizer Theorem says: If G is a finite group of permutations acting on a set S, then, for any element i of S, the order of G equals the product of the order of the orbit of i under G with the order of the stabilizer of i in G. The proof involves using Lagrange's Theorem and defining a one to one correspondence (bijection) between the set of left cosets of the stabilizer in G and the orbit of i under G.

#AbstractAlgebra #GroupTheory #LagrangeTheorem

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