Let $\,n\in\mathbb{N}\,$ and $p$ a prime. Let $P$ be a Sylow $p$-subgroup of $\,S_n\,$. If $p$ does not divide $n$, then $\,P\leq S_{n-1}\,$. Why?
An elementary fact about Sylow subgroup of Sym(n)
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group-theory
symmetric-groups
sylow-theory
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0@user I agree, wholeheartedly. It was Asaf who called me out on it. I think I'll continue adding it (and allow others to add it too), since I don't believe there is community consensus on the matter, and until the tag description changes (if it changes), I'll simply appeal to your logic, though I won't literally "point" to you. I'll just write out the tag description, as did you. – 2013-11-10