Nice Sylow Problem

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• Nov 7th 2007, 05:29 PM
ThePerfectHacker
Nice Sylow Problem
Here is a problem that I really like. I found it in an algebra book.
(It is nice, because if approached properly the proof is a one liner).

"Show that if $p$ divides $|Z(G)|$ then every Sylow $p$-subgroup of $G$ contains the Sylow $p$-subgroup of $Z(G)$".