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\subsection*Exercise 3 Let $G$ act on $A$. Prove that the kernel of the homomorphism $\varphi: G\to S_A$ is $\bigcap_a\in A G_a$, where $G_a = \g \in G \mid g\cdot a = a\$ is the stabilizer of $a$.

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: Groups acting on themselves by conjugation (the Class Equation). Section 4.4 : Automorphisms and the action of on its subgroups. \subsection*Exercise 3 Let $G$ act on $A$