Order of Power of Group Element/Examples/Powers of Element of Order 20

Example of Order of Power of Group Element
Let $G$ be a group.

Let $x \in G$ be such that:
 * $\order x = 20$

where $\order x$ denotes the order of $x$ in $G$.

Then:

Proof
From Order of Power of Group Element:


 * $\order {x^m} = \dfrac {\order x} {\gcd \set {m, \order x} }$

Here we have that $\order x = 20$.

Thus: