Infinite group whose every element is of order $4$?

Question

I have constructed infinite group whose every element is of prime order by taking the set as set of sequences whose elements are from integers modulo $p$ and operation is integers modulo $p$.

Now how can I get an infinite group whose every element is of order $4$ (non prime) except identity?.

Is there any general way of finding an infinite group whose every element is of order $n$?

Answer 1

Suppose $\lvert a\rvert=4$ for some $a\in G$ for some group $G$. Then $(a^2)^2=e$ and $a^2$ is non-trivial, so $$\lvert a^2\rvert=2.$$