Order of Power of Group Element/Examples

Examples of Order of Power of Group Element

Order of Powers of $x$ when $\order x= 20$

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:

\(\text {(1)}: \quad\)

\(\ds \order {x^4}\)

\(=\)

\(\ds 5\)

\(\text {(2)}: \quad\)

\(\ds \order {x^{10} }\)

\(=\)

\(\ds 2\)

\(\text {(3)}: \quad\)

\(\ds \order {x^{12} }\)

\(=\)

\(\ds 5\)