The Span Of A Set Of Permutations Is Closed

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Problem 24 (The Span Of A Set Of Permutations Is Closed)

Let $S$ be a set of permutations of $X$. Show that $\text{span}(S)$ is closed. In other words, show that once you form the span of a set $S$ of permutations of $X$, you cannot obtain any new permutations by spanning the span. For this reason, we'll often refer to $\text{span}(S)$ as the closure of $S$.

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