Let \(G\) be a group with identity \(e\) and \(g\in G\). If \(g^n=e\) for some integer \(n\geq 1\), the order of \(g\), written \(o(g)\), is the smallest such \(n\). If no such \(n\) exists, \(g\) has infinite order.
Order of a group element
D-ZTPHF
D-ZTPHF
Let \(G\) be a group with identity \(e\) and \(g\in G\). If \(g^n=e\) for some integer \(n\geq 1\), the order of \(g\), written \(o(g)\), is the smallest such \(n\). If no such \(n\) exists, \(g\) has infinite order.