Category:Examples of Order of Power of Group Element

This category contains examples of Order of Power of Group Element.

Let $\struct {G, \circ}$ be a group whose identity is $e$.

Let $g \in G$ be an element of $G$ such that:

$\order g = n$

where $\order g$ denotes the order of $g$.

Then:

$\forall m \in \Z: \order {g^m} = \dfrac n {\gcd \set {m, n} }$

where $\gcd \set {m, n}$ denotes the greatest common divisor of $m$ and $n$.