Let $G$ be a finite group and $P$ be a Sylow 2-subgroup of $G$. Let $N$ be a subgroup of $P$ of order two. If $|P|>8$, then is $N$ normal in $G$?
2026-03-24 23:44:34.1774395874
A normal minimal subgroup in a Sylow 2-subgroup
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Hint:
For any $\;n\ge3\;,\;\;Z(S_n)=1\;$ , meaning: the center of any permutation group of order $\;\ge4\;$ is trivial.