Let H = { S5
Chapter 5, Problem 38E(choose chapter or problem)
Let \(H=\left\{\beta \in S_{5} \mid \beta(1)=1 \text { and } \beta(3)=3\right\}\). Prove that H is a subgroup of \(S_5\). How many elements are in H? Is your argument valid when \(S_5\) is replaced by \(S_n\) for \(n \ge 3\)? How many elements are in H when \(S_5\) is replaced by \(A_n\) for \(n \ge 4\)?
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