Let G be a group of permutations on the set {1, 2, . . . ,
Chapter 8, Problem 50SE(choose chapter or problem)
Let G be a group of permutations on the set \(\{1,2, \ldots, n\}\). Recall that \(\operatorname{stab}_G(1)=\{\alpha \in G \mid \alpha(1)=1\}\). If \(\gamma\) sends 1 to k, prove that \(\gamma \operatorname{stab}_G(1)=\{\beta \in G \mid \beta(1)=k\}\)
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