Order of Finite Abelian Group with p+ Order p Elements is Divisible by p^2/Examples

Examples of Order of Finite Abelian Group with $p+$ Order $p$ Elements is Divisible by $p^2$

Order $3$

Let $G$ be a finite abelian group whose identity is $e$.

Let $G$ have more than $2$ elements of order $3$.

Then:

$9 \divides \order G$

where:

$\divides$ denotes divisibility

$\order G$ denotes the order of $G$.