Exponent of a group

Remarks

When the exponent is finite, it is the least common multiple of the orders of the elements of $G$. The exponent of a finite group divides the order of the group, by Lagrange's theorem. The exponent of the cyclic group of order $n$ is $n$, and the exponent of the Klein four-group is $2$. The exponent of $(\mathbb{Z}/n\mathbb{Z})^\times$ is the Carmichael function $\lambda(n)$.