I understand that $a \in Z (G)$ by this proof: Group question: only one element $x$ with order $n>1$, then $x\in Z(G)$ But I don't understand why $n$ must be equal to $2$?
2026-04-03 13:50:07.1775224207
If a group has only one element $a$ of order $n$, then $a$ belongs to $Z (G)$ and $n=2$.
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Hint What is the order of $a^{-1}$?