Every Finite Group is a torsion group?
I am learning about finitely generated groups at the moment and in the text book, they mention torsion groups, which they give the definition as:
A group $G$ is a torsion group if every element of $G$ is of finite order.
They then go on to state, when listing examples of torsion groups, that
"Every finite group is a torsion group"
I understand how cyclic groups would be a torsion group, but I am having trouble understand how a finite permutation group would be a torsion group. If anyone could help clarify why, it would be greatly appreciated.
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$\begingroup$The order of an element $g$ is the cardinality of $\langle g \rangle$, the cyclic group generated by it.
Every element $g$ in a finite group $G$ has finite order because $\langle g \rangle \subseteq G$ implies that $\langle g \rangle $ is finite.
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